Consider the function given by the graph. What are
these values?
fl-2) =
10) =
f(4) =
Answers
Answer:
f(-2) = 2
f(0) = 4
f(4) = -1
Step-by-step explanation:
Given the graph of a piecewise function:
[tex]\displaystyle\mathsf{f(x) = \left \{ {{x\:+\:4\quad if\:\:x\leq \:0} \atop {-\frac{1}{2}x\:+\:1\quad if\:\:x\: >\:0}} \right.}\\[/tex]
Side note:
I used the method of finding the linear equations in slope-intercept form to establish the piecewise function. First, I solved for the slope by choosing two points in each defined interval. Then, I plugged in the y-intercepts of each interval, for f(x) = x + 4: the y-intercept is (0, 4) where b = 4; for f(x) = -½x + 1, the y-intercept is (0, 1) where b = 1.
Explanation:There are two methods for determining the range values of the given domain values.
Method 1: The first method is using the graph to find the corresponding range values of the given domain {-2, 0, 4}.
Method 2: Alternatively, we could use the rules provided by the piecewise function in evaluating the following domain values. This post will use the second method (using the piecewise function) to evaluate the input values.
Regardless of the method used, the results will remain the same.
f(-2)Since the input value is x = -2, then we must use the function, f(x) = x + 4:
f(x) = x + 4
f(-2) = -2 + 4
f(-2) = 2
Therefore, the range value given the domain, x = -2 is 2, or simply: f(-2) = 2.
f(0)
Given the input value is x = 0, then we must also use the function, f(x) = x + 4:
f(x) = x + 4
f(0) = 0 + 4
f(0) = 4
Therefore, the range value given the domain, x = 0 is 4, or f(0) = 4.
f(4)
Since the input value is x = 4, then we must use the function, f(x) = -½x + 1:
f(x) = -½x + 1
f(4) = -½(4) + 1
f(4) = -2 + 1
f(4) = -1
Therefore, the range value given the domain, x = 4 is -1, or f(4) = -1.
Related Questions
PLEASE FIND THE MEASURE OF X
Answers
Answer: 3.42
Step-by-step explanation: use trig equations. Sin 20 = x/10. Multiply both sides by 10. Sin (20) times 10 is 3.42
Answer:
x = 3.42
Step-by-step explanation:
For the 20° angle, x is the opposite leg.
10 is the hypotenuse.
sin A = opp/hyp
sin 20° = x/10
x = 10 × sin 20°
x = 3.42
PLA HELP PLS PLS PLA
Answers
Answer:
y=3x-1
Step-by-step explanation:
I solved it by using graph paper so if you start out at (2,4), and go down 3 and left 1 you would end up at (-1,3)
Andrew measured a line to be 11 inches long. If the actual length of the line is 11.4 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
Answers
Answer:
3.5
Step-by-step explanation:
Error=11.4-11=0.4
Percentage error = (0.4/11.4) × 100 = 3.5 to the nearest tenth
The percent error in estimate is 3.5%
What is error?In practical mathematics, error is the distinction between a true value and an approximation, or approximate, representation of that value. A common example in statistics is the difference between the mean of the entire population and the mean of a sample picked from that population. An example of a round-off error in numerical analysis is the difference between an irrational number's actual value and the value of rational expressions.
Given
measured value = 11 inches
actual value = 11.4 inches
percent error = ((actual value - Estimate value)/actual value)100
percent error = ((11.4 - 11)/11.4)100
percent error = 0.03508 x 100
percent error = 3.508% = 3.5%
Hence the percent error is 3.5%.
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A map was made with a scale in which 3 inches represents 450 miles. The actual distance between two cities is 1,350 miles. What is the distance between the same two cities on the map?6 inches
Answers
Answer:
Step-by-step explanation:
(450 miles/3 inches) = 150 miles/inch
(1,250 miles)/(150 miles/inch) = 8.3333 inches
When the actual distance between two cities is 1350 miles the distance between the same cities on the map is 9 inches.
What is proportion?A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio.
Given that,
On scale 3 inches represents the actual distance = 450 miles.
To find the distance on scale when actual distance = 1350
Since, 3 inches = 450 miles
1 inch = 450 / 3 = 150 miles
150 miles = 1 inches
1 mile = / 1/ 150 inches
1350 miles = 1350 / 150 inches = 9 inches
The required distance on scale is 9 inches.
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simplify if y<0.
[tex]-\sqrt{9y^{2} }[/tex]
Answers
Answer:
-3y
Step-by-step explanation:
Whether y is smaller than 0 or not, the square root of y^2 is y, a positive quantity.
Thus, -√(9y²) = -3y
Answer
It's actually 3y instead of -3y.
BTW, anybody from RSM
woud
Unit 6 Portfolio
Task 1:
Taxi Cab Company A: $8 per ride and $0.35 per mile
• Write an equation in slope intercept form to represent the cost of a
taxi ride using company A.
Hint: use y=mx+b
Y =
• What does the y-intercept mean in the context of this problem?
Hint: What do you pay to step into the cab?
Answers
The y intercept means that $8 must be paid to step into the cab.
A linear equation is of the form:
y = mx + b
where y, x are variables, m is the slope of the line and b is the y intercept.
Let y represent the total pay for x miles
Since $8 per ride and $0.35 per mile, hence the equation is:
y = 0.35x + 8
The y intercept means that $8 must be paid to step into the cab.
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3 2/7 divided by 1 1/4
Answers
Answer:
92/35
Step-by-step explanation:
⇒ 3 2/7 ÷ 1 1/4
⇒ (3*7 + 2) / 7 ÷ (1*4 + 1) / 4
⇒ 23/7 ÷ 5/4
⇒ 23 * 4 / 7 * 5
⇒ 92/35
The solution of the expression is 2 22/35.
What is Division method?
Division method is used to distributing a group of things into equal parts.
Given that;
The expression is,
3 2/7 divided by 1 1/4
Now, Solve the expression as;
3 2/7 ÷ 1 1/4
23/7 ÷ 5/4
23/7 x 4/5
92/35
2 22/35
Hence, The solution of the expression is 2 22/35.
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A car was traveling at 25 m/s when it slammed on the brakes and came to a complete stop in 3 seconds. What is the cars INITIAL/FINAL VELOCITY?
Answers
Answer:
Initial velocity = 25 m/s
Final velocity = 0 m/s
Step-by-step explanation:
Initial velocity is the speed in the beginning and final velocity is the speed in the end.
The problem says the car was traveling at 25 m/s, so that is the initial velocity. The end of the problem states the car came to a complete stop after 3 seconds. Therefore, the final velocity is 0 m/s.
solve 3+x>-9 A) x >3 B) x > -6 C) x>-3 x > D) x> -3
Answers
Answer: the answer should be x>-12
Step-by-step explanation:
3+x>-9
x>-9-3
X>-12
I got this problem solved so I no longer need help
Answers
Answer:
then whats the point
Step-by-step explanation:
Evaluate the expression for x=2 and y=4
16x0 + 2x2 • y-1
Answers
Answer:
31
Step-by-step explanation
16x0+2x2•y-1
ok now
16•2+2•2•2•4-1
wich is: 31
What is the slope of the line that passes through the points (3, 7), (9, 19) and (5, 11)?
Answers
Answer:
the slope is 2
Step-by-step explanation:
use the slope formula which is y2-y1/x2-x1
You need to collect at least 32 shells to create a necklace. Your friend gave you 14 and you already had 6. How many more shells do you need to make a necklace? *
Answers
What will be the length of cloth used to make each bag, if 16 bags of equal sizes can be prepared from 50 m cloth?
A) 3 1/4 m
B) 8 1/6 m
C) 8 1/3 m
D) 3 1/8 m
Answers
Answer:
3 1/8
Step-by-step explanation:
16 bags = 50 m
1 bag = 50/16
1 bag = 25/8
1 bag = 3 1/8 ( due to mixed fraction )
so the cloth needed to make one bag is 3 1/8 m
how do you solve this linear programming inequality equation?
1 > 3P + 10
Answers
Answer:
-3 > P
Step-by-step explanation:
1 > 3P + 10
Subtract 10 from each side
1-10 > 3P + 10-10
-9 > 3P
Divide each side by 3
-9/3 > 3P/3
-3 > P
Multiply as indicated. Write the product in standard form. An explanation is needed.
(2+i)^2
Answers
Answer:
2^2 + i^2 or 4 + i^2 (depending if the teacher wants it simplified or not)
Step-by-step explanation:
(2+i)^2
Basically just add the power to each number using the distributive property. 2 would go to 2^2 (which can be simplified to four) and i would go to i^2.
Which ordered pair is a solution of the equation?
7x-2y=-57x−2y=−5
Answers
Answer:
what ordered pairs?
Step-by-step explanation:
Find the slope of each line.
Answers
Answer:
Step-by-step explanation:
There are 4 conditions that have to be met before you can declare what the slope is.
1. y has to be on one side of the equation.
2. y must have a coefficient of +1
3. the other side contains the x value. It can have any number as the slope which is in front of x.
4. The value of the number by itself which is not connected to x or y can also be any value including the irrational numbers.
Examples
y = 5x + 4
slope = 5
y intercept = 4
y = πx + sqrt(5)
slope = pi
y intercept = sqrt(5)
Answer to your question
slope = 7/5
y intercept = 5
Jason gets 15 gallons of gas at $3.90 a gallon. 15 gallons gives him 20 miles to the gallon. How many miles can Jason travel on 1 tank of gas?
Answers
Solve for the unknown side of each right triangle
Answers
x is 9.1 accordingly to the phytagores therom
List numbers that are between -103 ad -130
Answers
Answer:
104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123,124,125, 126, 127, 128, 129
Hello! :)
Numbers between -103 and -130:
-104-105-106-107-108-109-110-111-112-113-114-115-116-117-118-119-120-121-122-123-124-125-126-127-128-129These are the numbers between -103 and -130. Hope it helps. Please ask if you have any query.
~An excited gal
#CarryOnLearning
[tex]MagicalNature[/tex]
3.03Quiz:circles
The center of a circle lies on the line y=6x+2 and is tangent to the x-axis at (-2,0)
What is the equation of the circle in standard form?
Answers
Answer:
yung nasa pic sagut sa⇩
The center of a circle lies on the line y=6x+2 and is tangent to the x-axis at (-2,0)
What is the equation of the circle in standard form?⇩
-Standard form for the equation of a circle is (x−h)2+(y−k)2=r2. The center is (h,k) and the radius measures r units. To graph a circle mark points r units up, down, left, and right from the center.
thank me later♡
Find the sum of 382 - 8 - 10 and 1042 +2 - 10.
Answers
Answer:
364 and 1034
Step-by-step explanation:
How to convert minutes and seconds into grades.
Answers
Answer:
Step-by-step explanation:
To convert time to time, kernel time with 24 (number of time in a day).
To convert time to minutes, kernel with time with 1440 (number of minutes in a day = 24 * 60).
To convert s to seconds, multiply the time by 86400 (number of s in a day = 24 * 60 * 60).
Evaluate.
(2a - 3) ÷ (b / 4) when a = 12 and b = - 20
Answers
Answer:
-4.2
Step-by-step explanation:
First me put a and b in
2x12
24
(24 - 3) = 21
b: -20
-20 divided by 4 = -5
21 divided by -5
Answer= -4.2
what is the value of a in a/5 + 3= 8
Answers
Answer:
Step-by-step explanation:
what is the value of a in a/5 + 3= 8
a/5 + 3= 8
a/5 = 8 - 3
a/5 = 5
a = 5 * 5
a = 25
Answer: a= 25
Step-by-step explanation:
first, you'll have to write the opposite of the + symbol which is - and then you'll have to lose the 3 by substracting it with, so the equation will look like this: a/5= 8-3 not 8+3
a/5=5
after that step you'll have to multiply 5 from the equal sgin with the 5 that is divided by a, so the final equation looks like this:
a=5x5
a=25
now let's make a verification:
25/5+3=8
5+3=8
a=25
hope I helped you :)
What is the distance between the points (-3, 5) and (-3, -6) on the coordinate plane?
Answers
Explanation (x-x) + (y-y)
please help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee (thank you :)
(cAt)
Answers
Answer:
answer is 2
Step-by-step explanation:
funny pic
Write your answer as a decimal. If the decimal has more than 2 decimal places, round to 2 decimal places.
Answers
hey can someone help with my assignment worth 80% of my grades
Answers
Answer:
Honestly the intercept should be on the axis
Step-by-step explanation:
Answer:
You didn't helped me with my question so no
Step-by-step explanation: