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From the given functions, let's select the functions that are one-to-one functions.
A function is said to be a one-to-one function when it produces different outputs for different inputs (values of x).
The easiest way to determine if a function is a one-to-one function is to graph the function and use the horizontal line test.
Now, let's check the functions to determine.
• Function 1.
f(x) = x³ - 7
Since the leading exponent is an odd number, this function can be said to be a one-to-one function.
• Function 2.
f(x) = x² - 4
The leading exponent of this function is an even number. Since it is even, it will fail the horizontal line test. Therefore, the function is NOT a one-to-one function.
• Function 3.
[tex]f(x)=\frac{1}{8x-1}[/tex]This function is a one-to-one function.
• Function 4.
[tex]f(x)=\frac{5}{x^4}[/tex]This function is a one-to-one function.
• Function 5.
f(x) = |x|
This function is NOT a one-to-one function since it will fail the horizontal line test.
Therefore, the functions that are one-to-one are:
[tex]\begin{gathered} f(x)=x^3-7 \\ \\ f(x)=\frac{1}{8x-1} \\ \\ f(x)=\frac{5}{x^4} \end{gathered}[/tex]
Related Questions
120 people were asked to choose their favorite colorfrom a list of 6 colors. 18 people chose orange. Findthe degree measure of the part of the circle graph thatrepresents orange?
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You have 120 people as a total, of which 18 choose orange. This ratio of people can be represented as 18/120. This equals to 3/20, which means that for every 20 persons, 3 of them choose orange. You also know that a full circle has 360 degrees. You need to find how many "orange" degrees you have for every 360. 360/20 equals 18, so in 360 degrees you have 18 pieces of 20 degrees each. This means that every 20 degrees, 3 of them will be orange. 3*18 is 54. You can check this by seeing that 54/360 equals to 3/20. Concluding, 54 degrees of a circle graph represents orange.
Please guide me in the correct direction with attached pic. For p(x)=7+10x-12x^2-10x^3+2x^4+3x^5, evaluate the following;
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Solution:
Given:
[tex]p(x)=7+10x-12x^2-10x^3+2x^4+3x^5[/tex]To find p(-3), substitute x = -3
[tex]\begin{gathered} p\left(x\right)=7+10x-12x^2-10x^3+2x^4+3x^5 \\ p(-3)=7+10\left(-3\right)-12\left(-3\right)^2-10\left(-3\right)^3+2\left(-3\right)^4+3\left(-3\right)^5 \\ p(-3)=-428 \end{gathered}[/tex]To find p(1), substitute x = 1
[tex]\begin{gathered} p\left(x\right)=7+10x-12x^2-10x^3+2x^4+3x^5 \\ p(1)=7+10\cdot\:1-12\cdot\:1^2-10\cdot\:1^3+2\cdot\:1^4+3\cdot\:1^5 \\ p(1)=0 \end{gathered}[/tex]To find p(5), substitute x = 5
[tex]\begin{gathered} p\left(x\right)=7+10x-12x^2-10x^3+2x^4+3x^5 \\ p(5)=7+10\cdot\:5-12\cdot\:5^2-10\cdot\:5^3+2\cdot\:5^4+3\cdot\:5^5 \\ p(5)=9132 \end{gathered}[/tex]Therefore, OPTION B is correct.
A coin-operated coffee machine made by BIG Corporation was designed to discharge a mean of eight ounces of coffee per cup. If it dispenses more than that on average, the corporation may lose money, and if it dispenses less, the customers may complain.BIG Corporation would like to estimate the mean amount of coffee, μ, dispensed per cup by this machine. BIG will choose a random sample of cup amounts dispensed by this machine and use this sample to estimate μ. Assuming that the standard deviation of cup amounts dispensed by this machine is 0.35 ounces, what is the minimum sample size needed in order for BIG to be 90% confident that its estimate is within 0.07 ounces of μ?Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements).
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Population mean: μ is 8 ounces.Population standard deviation: σ is 0.35 ounces. Margin of error: 0.07 so n is equal to 96.04
What is the population mean?Population mean: μ is 8 ounces.Population standard deviation: σ is 0.35 ounces. Margin of error: 0.07 so n is equal to 96.04
E = z(0.025)0.4/√n < 0.06
then
z(0.025)=1.96
where
1.96(0.35)/0.07 < √n
n > (1.96(0.35)/0.07)^2 =96.04:
so n is equal to 96.04
n=96
The population mean can be determined by dividing the total number of values in the given data/population by the sum of all values in the data/population. The whole sum of the numbers is referred to as summation. The sign stands for the population mean.
It is determined using the population's total values, represented by the sum of X divided by the total number of population values, represented by N.
To learn more about population mean refer to:
https://brainly.com/question/19426829
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Find the slope of a line given the table of value below answer in a simplified fraction if necessary
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Use any two ordered pair in the table, to solve for the slope. In this instance, we will be using (1,-11) and (6,-20)
[tex]\begin{gathered} m=\dfrac{y_2 - y_1}{x_2 - x_1} \\ m=\dfrac{-20-(-11)}{6-1} \\ m=\dfrac{-20+11}{5} \\ m=\frac{-9}{5} \\ \; \\ \text{Therefore, the slope of the line is }m=-\frac{9}{5} \end{gathered}[/tex]IITT STUw your Given Triangle ABC A(1,2) B(3,5) C(2,7) --------> You must graph this lidligi -> You must graph this triangle Translate by the rule (-5,-6). --> You must graph this triangle Then reflect over the y-axis -- **There should be three triangles on your graph**
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The given triangle has points A(1, 2), B(3, 5), and C(2, 7)
When the triangle is translated by the rule (-5, -6), the new points of the triangle becomes:
A'(1-5, 2-6) = A'(-4, -4)
B'(3-5, 5-6) = B'(-2, -1)
C'(2-5, 7-6) = C'(-3, 1)
Summarily, the points after translation of the triangle by the rule (-5, -6) are A'(-4, -4), B'(-2, -1), C'(-3, 1)
Then the triangle is reflected over the y-axis:
When a triangle is reflected over the y-axis, the coordinates of the y-axis remains the same, but the coordinates of the x-axis is negated.
The new points ofthe triangle after reflection therefore become:
A''(4, -4), B''(2, -1), C''(3, 1)
The three triangles(that is, the original, after translation, and after reflection) are plotted below
Estimate 8535/34 by first rounding each number so that it has only 1 nonzero digit.
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Answer: The estimated answer, or in the simplest terms is as follows:
[tex]\begin{gathered} \frac{8535}{34}=\frac{8540}{30}=\frac{854}{3} \\ \\ =\frac{854}{3} \end{gathered}[/tex]I need help the second problem I don’t get this concept?
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In general,
[tex]\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}[/tex]In our case,
[tex]\frac{3}{4}+\frac{1}{8}=\frac{3*8+1*4}{4*8}=\frac{24+4}{32}=\frac{28}{32}[/tex]Simplifying,
[tex]\begin{gathered} \frac{28}{32}=\frac{4*7}{4*8}=\frac{4}{4}*\frac{7}{8}=1*\frac{7}{8}=\frac{7}{8} \\ \Rightarrow\frac{3}{4}+\frac{1}{8}=\frac{7}{8} \end{gathered}[/tex]The simplified answer is 7/8.
a) Given
[tex]\frac{1}{2}+\frac{2}{3}+\frac{9}{2}[/tex]Notice that
[tex]\frac{1}{2}+\frac{2}{3}+\frac{2}{9}=(\frac{1}{2}+\frac{2}{3})+\frac{2}{9}[/tex]First, calculate the term between parentheses
[tex]\frac{1}{2}+\frac{2}{3}=\frac{1*3+2*2}{2*3}=\frac{3+4}{6}=\frac{7}{6}[/tex]Then,
[tex]\begin{gathered} \Rightarrow\frac{1}{2}+\frac{2}{3}+\frac{2}{9}=\frac{7}{6}+\frac{2}{9}=\frac{7*9+2*6}{6*9}=\frac{63+12}{54}=\frac{75}{54} \\ \Rightarrow\frac{1}{2}+\frac{2}{3}+\frac{2}{9}=\frac{75}{54} \end{gathered}[/tex]Simplifying,
[tex]\begin{gathered} \frac{75}{54}=\frac{3*25}{3*18}=\frac{25}{18} \\ \Rightarrow\frac{1}{2}+\frac{2}{3}+\frac{2}{9}=\frac{25}{18} \end{gathered}[/tex]The answer to (a) is 25/18
(b)
[tex]\begin{gathered} \frac{2}{3}*\frac{42}{5}*\frac{10}{7}=(\frac{2}{3}*\frac{42}{5})*\frac{10}{7}=(\frac{2*42}{3*5})*\frac{10}{7}=\frac{84}{15}*\frac{10}{7}=\frac{840}{105}=8 \\ \Rightarrow\frac{2}{3}*\frac{42}{5}*\frac{10}{7}=8 \end{gathered}[/tex]The answer to part (b) is 8.
The difference in speeds of Son of Beast and the Rattler is 13 miles per hour. If son of Beast has the greater speed, write and solve a subtraction equation to find its speed.Son of Beast = sRattler = 65mph
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given
[tex]\begin{gathered} s-65=13 \\ s=78 \end{gathered}[/tex]So speed of son of beast is 78 mph
Trying to double check my work just need final answer.
Answers
Explanation
In answering the question, we will make use of the fact that
For option 1
[tex]\begin{gathered} F(x)=\frac{2x-1}{3x^2} \\ The\text{ horizontal asymptote is} \\ y=0 \end{gathered}[/tex]For option 2
[tex]\begin{gathered} f(x)=\frac{x-1}{3x} \\ \\ The\text{ horizontal assymptote is} \\ y=\frac{1}{3} \end{gathered}[/tex]For option 3
[tex]\begin{gathered} f(x)=\frac{2x^2}{3x-1} \\ \\ There\text{ is no horizontal asymptote} \end{gathered}[/tex]For option 4
[tex][/tex]908.64 is 45% of monthly income.what is total income?
Answers
ANSWER
2019.20
EXPLANATION
We know that 908.64 is 45% of the monthly income. The total income is the 100%, so we have to find how much is 100%,t
[tex]908.64\cdot\frac{100}{45}=2019.20[/tex]Hence, the total income is 2019.20.
I need help with this please! This is Geometry :)
Answers
16.
Answer:
The coordinates of the image points are;
[tex]\begin{gathered} F^{\prime}(-3,0) \\ G^{\prime}(-3,2) \\ U^{\prime}(1,4) \\ W^{\prime}(1,2) \end{gathered}[/tex]Explanation:
We want to find the coordinates of the image of given shape after 90 degree counterclockwise rotation.
The rule for 90 degree counterclockwise rotation about the origin can be written as;
[tex](x,y)\rightarrow(-y,x)[/tex]Firstly, let us write out the coordinates of the preimage points;
[tex]\begin{gathered} F=(0,3) \\ G=(2,3) \\ U=(4,-1) \\ W=(2,-1) \end{gathered}[/tex]We can now apply the rule to determine the coordinates of the image points;
[tex]\begin{gathered} (x,y)\rightarrow(-y,x) \\ F(0,3)\rightarrow F^{\prime}(-3,0) \\ G(2,3)\rightarrow G^{\prime}(-3,2) \\ U(4,-1)\rightarrow U^{\prime}(1,4) \\ W(2,-1)\rightarrow W^{\prime}(1,2) \end{gathered}[/tex]Therefore, the coordinates of the image points are;
[tex]\begin{gathered} F^{\prime}(-3,0) \\ G^{\prime}(-3,2) \\ U^{\prime}(1,4) \\ W^{\prime}(1,2) \end{gathered}[/tex]3120 fans attended the final game of the season this was a 30% increase from the attendance at the first game of the season how many fans attended the first game of the season
Answers
let the number of attended the first game is x
30 % increment of x = 3120 ......( Given)
x + 30 % of x = 3120
[tex]\begin{gathered} x+x\times\frac{30}{100}=3120 \\ \frac{130x}{100}=3120 \end{gathered}[/tex][tex]\begin{gathered} x=\frac{31200}{13} \\ x=2400 \end{gathered}[/tex]thus, the answer is 2400 fans attended first game
What is expression on mathematics??
Answers
Explanation:
An expression in math is composed of numbers, arithmetic operators, and it also can have variables.
An expression can have the following components:
Coefficient
Variable terms
Constant terms
Arithmetic operators
Where the coefficient is the number that accompanies the variables, the variable terms are the ones that have a letter, constant terms consists of only a number without variable, and the arithmetic operators can be +, - /, x, etc.
For example, an expression can be:
[tex]\begin{gathered} 10-8 \\ \end{gathered}[/tex]or
[tex]-5\times9[/tex]These expressions have numbers and arithmetic operators.
The expressions can also have variables, for example:
[tex]8x-3[/tex]Or it can have more terms:
[tex]9x^2+6x-1[/tex]It is important to state that expressions don't have an equal symbol (=), in that case, it is called an equation.
Answer: An expression in math is composed of numbers, arithmetic operators, and it also can have variables.
Juan earns $11.75 for each lawn he mows, and it takes him as of an hour to mow each lavvn. Which expression represents the number of hours it takes Juan to earn $141? o 141 – 11.75 x = 133 0 141 = x 11.75 = 2485 0 141 +11.75 = { = 228 o 141 = 11.75 x š = 8
Answers
E = 11.75t
t = number of hours or x
141 = 11.75x This is the answer
The first one is the answer
Example 1: Let f(x) = x2 +3. Evaluate f(x) at x = -1, 0, and 2. Make a table using these values.
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the given function is:
[tex]f(x)=x^2+3[/tex]If x = -1, then:
[tex]f(x)=(-1)^2+3=1+3=4[/tex]if x = 0, then:
[tex]f(x)=0^2+3=3[/tex]If x = 2 then:
[tex]f(x)=2^2+3=4+3=7[/tex]So, a table with the values of x and f(x) is:
Background Layout PERCENT OF CHANGE Directions 12 to 13.26 10.5% Increase: yellow 10.53 decrease: white 110.5% increase: pink decrease: green 65% decrease: yellow 40 to 26 35% decrease: blue Determine the percent of change and if there is an increase or decrease. Drag a round rectangle piece onto the answer. 35% increase: orange increase: white 60 to 84 140% increase: orange 140% decrease: red 71.4% increase: yellow increase: Pink 12.5 to 18.75 50% increase: white 150% increase: yellow 150% decrease: blue 50% decrease: green Go to the coloring page and follow the directions. coloring page NAME: 26% increase: 50 to 37 increase: pink 26% decrease: blue decrease: yellow
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Here, we want to get the percentage increase or decrease
At any point in time, we have the percentage change as;
[tex]\frac{new\text{ value -old value}}{\text{old value}}\times\text{ 100 \%}[/tex]The key to know if there is an increase or a decrease is that if the old value is bigger than the new value, there is a decrease, but otherwise, there is an increase in percentage
a) 12 to 13.26
[tex]\frac{13.26-12}{12}\times\text{ 100 \% = 10.5 \%}[/tex]The correct answer here is 10.5% increase, so we use the yellow
b) 40 to 26
[tex]\frac{26-40}{40}\times100\text{ \% = -35\%}[/tex]This is a 35% decrease, so we select the blue
c) 60 to 84
[tex]\frac{84-60}{60}\times100\text{ \% = 40 \%}[/tex]This is 40% increase, and we use the pink
d) 12.5 to 18.75
[tex]\frac{18.75-12.5}{12.5}\times100\text{ \% = 50 \%}[/tex]That is a 50% increase and we select the white
e) 50 to 37
[tex]\frac{37-50}{50}\times\text{ 100 \% = -26 \%}[/tex]That is 26% decrease, and we select the blue
an office is 20 feet long
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Find volume V
Length L = 20 feet,
Width W= 15
Height H = 12
Volume V a= Lx Wx H = 20x15x12 = 3600 cubic foot
Then for 1 year , it costs = 3600x 9 cents= 32400 cents
For 1 month , (divide by 12) = 32400/12 = 2700
Then answer is
Aircondition this office ,for 1 month costs $2700 cents
A building has 15 floors of offices above ground and 3 floors below ground. Lucy parks on the 3rd floor below ground and has an office on the 10th floor. The ground floor is floor zero. How many floors must she go up from her car to her office? A 5 floors B 7 floors 12 floors D) 13 floors
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We can picutre the situation as follows
The ground floor is floor zero. So there are 15 more floors above. Let us suppose that she parks on the third floor under the ground. So, to find out the number of floors she has to go up, we simply subtract the number of the floor she is heading, and number of the floor she starts at. Since she starts at the third floor under ground, we can say that she starts at floor -3. In this case, we have that
[tex]\text{target floor - initial floor = 10-(-3) = 10+3 = 13}[/tex]So she has to go up 13 floors.
A pyramid has a base that is a right traingle with legs measuring 10 cm and 14 cm. The height of the pyramid is 9 cm.The volume of the pyramid is ___ cubic cm.
Answers
The volume formula is given by
V = 1/3 Bh where B is the area of the base and h is the height
The area of the base is the area of a triangle
B = 1/2 (10)*14 = 70 cm^2
V =1/3 (70cm^2) ( 9 cm)
C =210 cm^3
x= 1/2, y=4, z=1/420z+y3+40x(x-z)
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we want to find;
[tex]\begin{gathered} 20z+y^3+40x(x-z)\text{ -----(1)} \\ \text{ sustituting }x=\frac{1}{2};\text{ }y=4;\text{ }z=\frac{1}{4}\text{ in eqation (1)} \\ \Rightarrow20z+y^3+40x(x-z)=20(\frac{1}{4})+(4)^3+40(\frac{1}{2})(\frac{1}{2}-\frac{1}{4})=5+64+5 \\ \end{gathered}[/tex]Therefore, 20z+ y^3 + 40x(x-z) = 74.
subtractf(x) =-5x²+x-2g(x) = -3x²+3x+9
Answers
We are given the following functions:
[tex]\begin{gathered} f\mleft(x\mright)=-5x^2+x-2 \\ g\mleft(x\mright)=-3x^2+3x+9 \end{gathered}[/tex]we will find their difference.
[tex]f(x)-g(x)=-5x^2+x-2-(-3x^2+3x+9)[/tex]First, we will change the sign of the terms inside the parenthesis, since it is preceded by a minus sign:
[tex]=-5x^2+x-2+3x^2-3x-9[/tex]Now we will associate like terms, that is terms that have the same variable elevated to the same exponentÑ
Rewrite (6x3 + 9x2 + 7)/(2x3 + 3x2) in the form q(x) + r(x)/b(x) where q(x) = quotient, r(x) = remainder, and b(x) = divisor.
Answers
Given:
There is an expression given as below
[tex]\frac{6x^3+9x^2+7}{2x^3+3x^2}[/tex]Required:
We need to convert the given expression in form of q(x) + r(x)/b(x) where q(x) = quotient, r(x) = remainder, and b(x) = divisor.
Explanation:
Simplify the given equation
[tex]\frac{6x^3+9x^2+7}{2x^3+3x^2}=\frac{6x^3+9x^2}{2x^3+3x^2}+\frac{7}{2x^3+3x^2}[/tex]Simplify as
Final answer:
[tex]3+\frac{7}{2x^{3}+3x^{2}}[/tex]Evaluate the expression when h = -6. 19 + h
Answers
∵ h = -6
Replace h by -6 in the expression above
[tex]\therefore19+h=19+(-6)[/tex]19 + (-6) means 19 - 6
[tex]\begin{gathered} \therefore19+h=19-6 \\ \therefore19+h=13 \end{gathered}[/tex]The answer is 13
Translate to a system of equations:The sum of two numbers is twenty-four. The second number is equal to twice the first number. Call the first number m and the second number n."m+n=? " "n=?m"
Answers
Here is the statements:
"The sum of two numbers (m + n) is twenty-four (= 24)"
"The second number (n) is equal to twice the first number (= 2m)
Then we have:
m + n = 24
n = 2m
What is the value of x in the figure below? In this diagram, AABD - ACAD.B 509O A. 126OB. 45O c. 45O D.914O E. 170O F. 14
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The x in the figure is the altitude to the hypotenuse.
The length of the altitude to the hypotenuse is the square root of the product of the divided segment of the hypotenuse.
This will be :
[tex]\begin{gathered} x=\sqrt[]{5\times9} \\ x=\sqrt[]{45} \end{gathered}[/tex]The answer is Choice C. √45
How many solutions does the equation have?7(x - 2) = -14 + 7xA. Only 1 solution B. No solutionsC. Infinitely many solutions
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The equation is given as,
[tex]7(x-2)\text{ = -14 + 7x}[/tex]Opening the bracket,
[tex]\begin{gathered} 7x\text{ - 14 = -14 + 7x} \\ 0\text{ = 0 } \end{gathered}[/tex]Therefore the given equation is true for all x.
Thus the given equation has infinitely many solutions.
write the rule for the translation shown below using mapping notation
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From blue to red:
Take any point.
C
We can see that point C moves 5 units to the right and 1 unit up
x+5, y+1
Mapping notation:
T:(x,y) ⇒ (x+5,y+1)
Find the slope of the line that goes through the given points
Answers
The slope is -8
Explanation:The slope of a line passing through a point:
[tex](x_1,y_1),(x_2,y_2)[/tex]is given as:
[tex]M=\frac{y_2-y_1}{x_2-x_1}[/tex]For the given (-3, -8), (-5, 8), we have:
[tex]\begin{gathered} M=\frac{8-(-8)}{-5-(-3)} \\ \\ =\frac{8+8}{-5+3}=\frac{16}{-2}=-8 \end{gathered}[/tex]Using the diagram below, classify the angle pairs as corresponding. alternate interior, alternate exterior, consecutive interior, consecutive exterior, or none.1-) what classification corresponds to angle 6 and 7 angle.
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Because of the position of the angles, they are alternate exterior
Lashonda purchased a prepaid phone card for $20. Long distance calls cost 12 cents a minute using this card. Lashonda used her card only once to make a long distance call. If the remaining credit on her card is $17, how many minutes did her call last?
Answers
Given that the long distance calls cost 12 cents (i.e. $0.12) per minute.
Let Lashonda spent 'x' minutes on the call,
Then the associated cost is given by,
[tex]\begin{gathered} C=\text{Cost per minute}\times\text{ No. of minutes} \\ C=0.12\times x \\ C=0.12x \end{gathered}[/tex]Given that the total cost initially was $20, and the cost remaining after making the call is $17,
[tex]\begin{gathered} \text{Total Cost=Cost Spent on Call+Remaining Cost on Card} \\ 20=0.12x+17 \\ 0.12x=20-17 \\ 0.12x=3 \\ x=\frac{3}{0.12} \\ x=25 \end{gathered}[/tex]Thus, her call lasted for 25 minutes.