Express the function graphed on the axes below as a piecewise function.

Express The Function Graphed On The Axes Below As A Piecewise Function.

Answers

Answer 1

Answer:

  f(x) = {x-3 for x ≤ -1; -3x+14 for x > 5}

Step-by-step explanation:

To write the piecewise function, we can consider the pieces one at a time. For each, we need to define the domain, and the functional relation.

__

Left Piece

The domain is the horizontal extent. It is shown as -∞ to -1, with -1 included.

The relation has a slope (rise/run) of +1, and would intersect the y-axis at -3 if it were extended.

The first piece can be written ...

  f(x) = x-3 for x ≤ -1

__

Right Piece

The domain is shown as 5 to ∞, with 5 not included.

The relation is shown as having a slope (rise/run) of (-3)/(1) = -3. If extended, it would intersect the point (5, -1), so we can write the point-slope equation as ...

  y -(-1) = -3(x -5)

  y = -3x +15 -1 = -3x +14

The second piece can be written ...

  f(x) = -3x +14 for x > 5

__

Whole function

Putting these pieces together, we have ...

  [tex]\boxed{f(x)=\begin{cases}x-3&\text{for }x\le-1\\-3x+14&\text{for }5 < x\end{cases}}[/tex]

_____

Additional comment

Sometimes it is convenient to write inequalities in number-line order (using < or ≤ symbols). This gives a visual indication of where the variable stands in relation to the limit(s). Perhaps a more conventional way to write the domain for the second piece is, x > 5.


Related Questions

(4x^2+9x-7)-(-7x^2+5x-1)
(4x
2
+9x−7)−(−7x
2
+5x−1)

Answers

Step-by-step explanation:

I think the expression is

(4x² + 9x - 7) - (-7x² + 5x - 1)

and that is the same as

4x² + 9x - 7 + 7x² - 5x + 1 =

= 11x² + 4x - 6

remember that the combination of two '-' signs turns this into one '+' sign.

to subtract a negative number is indeed the same as adding a positive number with the same absolute value.

Find the volume of the figure. If necessary, round your answer to the nearest tenth.

Answer choices
A: 441.6 cm^3
B: 883.2 cm^3
C: 147.2 cm^3

Answers

Here is the answer and explanation I wrote:

Answer:

A

Step-by-step explanation

math

HELP PLEASEE!!!

A prism is filled with 25 cubes with 1/2-unit side lengths. What is the volume of the prism in cubic units?

Answers

Answer:

3.125 cubic unit i guess

Answer:

3.125 unit cube is the answer i hope i helped u

What is the volume of this cone? use 3.14 for π and round your answer to the nearest tenth. in your answer, give the volume of the cone rounded to the nearest tenth, and then explain how you calculated it.

Answers

Answer:

Volume of a cone = 1/3•pi r•r•h

V = 1/3•pi•2•2•8

V = 33.49333333333333

V = 33.5 inches squared

I hope this helps! Have a good day! :)

The volume of the considered cone whose heigth is 8 inches and radius of the base is 2 inches is 33.5 cubic inches approximately.

How to find volume of a right circular cone?

Suppose that the radius of considered right circular cone be 'r' units.

And let its height be 'h' units.

Then, its volume is given as:

[tex]V = \dfrac{1}{3} \pi r^2 h \: \rm unit^3[/tex]

Right circular cone is the cone in which the line joining peak of the cone to the center of the base of the circle is perpendicular to the surface of its base.

The missing image for this problem is attached below.

For this case, the radius is of 2 inches, and height is of 8 inches, thus, the volume of the considered cone is:

[tex]V = \dfrac{1}{3} \pi r^2 h \: \rm unit^3 \approx \dfrac{1}{3} \times 3.14 \times (2)^2 \times 8 \approx 33.51 \approx 33.5 \: \rm in^3[/tex]

(rounded to the nearest tenth, which is first place to right of the decimal point.

Thus, the volume of the considered cone whose heigth is 8 inches and radius of the base is 2 inches is 33.5 cubic inches approximately.

Learn more about volume of a cone here:

https://brainly.com/question/26093363

Find the area of the polygon.

Answers

Answer:

95 m

Step-by-step explanation:

you can split the shape into three pieces so it is 4x5, 4x5, and 11x5. Add the products for the area which is 95 m

Paul bought 4 DVDs for $9.95 each. What was his total cost?

A.$39.90

B.$40.80

C.$39.80

D.$38.80

Answers

I believe it’s C $39.80 $9.95 x 4

Errin bought stock in XYZ Corporation for $100 per share. One month later the stock was up 10%. After another month the stock fell 10%. a. What was the price of the stock after the first month? b. What was the price of the stock after the second month?​

Answers

Answer:

350 sum

Step-by-step explanation:

1. The equation of a circle is x² + y² - 4x +2y-11-0. What are the center and the radius of the circle?
www
Show your work.
Answer:

Answers

[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the concept of Circles,

so we get as,

centre as ==> ( -g, -f) ==> (2,-1)

How do i Write (3x^3)^2 WITHOUT exponents

Answers

Answer:

(3x³)² = 9x⁶ = 3 × 3 × x × x × x × x × x × x

Thus, The answer is

3 × 3 × x × x × x × x × x × x

Answer:

3 * 3 * y * y * y * y * y * y

Step-by-step explanation:

(3y³)²

Multiply 3 by 3 and y six times

3 * 3 = 9

y * y * y * y * y * y

The answer should be

3 * 3 * y * y * y * y * y * y

I hope this helps!

help its for calculus

Answers

Answer:

maybe its e(1/y)

Answer:

it should be e(1/y)

Evaluate (2 minus 5 i) (p + q) (i) when p = 2 and q = 5 i.



29 i

29 i - 20

- 21 i

29

Answers

(2 - 5i) (2 + 5i) (i)
(4 + 10i - 10i -25) (i)
(4 - 25) (i)
-21i

Ed Galaxy- Operations with whole numbers and decimals ​

Answers

Answer:

0.6

Step-by-step explanation:

1.0l-0.4l=0.6L

Multiple choice easy question. Please answer.

Answers

Answer:

I belive it should be # 3 i might be wrong thow.

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Car one rotated 90 degrees counterclockwise would be to car 4
then, it rotated 180 degrees clockwise would be car 2.

the answer is Car 2

Please Help Me ASAP.

Answers

Answer:

x > -10

Step-by-step explanation:

5 - 3x > 35

-5           -5

-3x > 30

[tex]\frac{-3x > 30}{-3}[/tex]= x > -10

Find x.
Round to the nearest tenth:
31°
у
X
400 ft
x = [ ? ]ft

Answers

Answer:

x = 466.7 fty = 240.3 ft

First find the inner angle:

90° - 31°59°

using sine rule:

[tex]\sf sin(x)= \dfrac{opposite}{hypotensue}[/tex]

[tex]\hookrightarrow \sf sin(59)= \dfrac{400}{x}[/tex]

[tex]\hookrightarrow \sf x = \dfrac{400}{sin(59)}[/tex]

[tex]\hookrightarrow \sf x = 466.6533[/tex]

[tex]\hookrightarrow \sf x = 466.7[/tex]   ( rounded to nearest tenth )

====================================

using tan rule:

[tex]\sf tan(x)= \dfrac{opposite}{adjacent}[/tex]

[tex]\hookrightarrow \sf tan(59)= \dfrac{400}{y}[/tex]

[tex]\hookrightarrow \sf y= \dfrac{400}{ tan(59)}[/tex]

[tex]\hookrightarrow \sf y= 240.344[/tex]

[tex]\hookrightarrow \sf y= 240.3[/tex]

Answer:

y = 466.7 ft (nearest tenth)

Step-by-step explanation:

Using the Alternate Interior Angle Theorem
the angle inside the triangle that is opposite the side [tex]y[/tex] is 31°

Using the cos trig ratio:

[tex]\sf cos(\theta)=\dfrac{A}{H}[/tex]

where:

[tex]\theta[/tex] is the angleA is the side adjacent the angleH is the hypotenuse

Given:

[tex]\theta[/tex] = 31°A = 400 ftH = [tex]x[/tex]

Substitute given values and solve for x:

[tex]\sf \implies cos(31)=\dfrac{400}{x}[/tex]

[tex]\sf \implies x=\dfrac{400}{cos(31)}[/tex]

[tex]\sf \implies x=466.7\:ft\:(nearest\:tenth)[/tex]

Determine the simple interest earned p=$2000 r=4.6% T=4 years

Answers

Answer:

[tex]\boxed{\sf{I=368}}[/tex]

Step-by-step explanation:

Use a simple interest formula.

Simple interest formula:

⇒ I=Prt

P stands for principal R stands for interest rateT stands for interest time

(P): Principal =$2000(R): Interest Rate =4.6%(T): Interest Time =4

→ 2000*4.6%4

You have to convert 4.6% into a decimal form.

→ 4.6%=0.046

→ I=2000*0.046*4

Solve.

Multiply the numbers from left to right.

→ 2000*0.046*4=368

Therefore, the correct answer is 368.

I hope this helps you! Let me know if my answer is wrong or not.

How much should you invest in an account that pays 6% annual interest compounded continuously if you want exactly $8000 after four years?

Answers

Answer:

$6239

Step-by-step explanation:

A(t) = P•e^rt

Substitute with 6% 0.06, t with 4 and A(t) with 8,000 to find the value of P.

8, 000 = P•e^0.06•4

8, 000 = P•e^0.24

8, 000 = P•1.27

P = 6, 293

Find the axis of symmetry and the vertex of the graph of the function.
g(x) = 2x^2+12x+4

Answers

so hmmm from the equation we can see that is in "x terms" so the independent variable is "x", that tells us the parabola is a vertical one, leading term's coefficient is "2", that means it opens upwards like a bowl.

on a vertical parabola the axis of symmetry is the x-coordinate of its vertex, let's find the vertex of this one.

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{2}x^2\stackrel{\stackrel{b}{\downarrow }}{+12}x\stackrel{\stackrel{c}{\downarrow }}{+4} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 12}{2(2)}~~~~ ,~~~~ 4-\cfrac{ (12)^2}{4(2)}\right)\implies \left( -3~~,~~4-\cfrac{144}{8} \right) \\\\\\ (-3~~,~~4-18)\implies (\stackrel{x}{-3}~~,~~-14)~\hfill \stackrel{\textit{axis of symmetry}}{x=-3}[/tex]

probability pls hurry(13)

Answers

Answer:

A (3/16)

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

The spinner is evenly divided and numbered from 1 through 8.

[tex]\sf \implies Probability\:of\:landing\:on\:any\:number= \dfrac18[/tex]

There are 4 even numbers (2, 4, 6 and 8)

[tex]\sf \implies Probability\:of\:landing\:on\:an\:even\:number= \dfrac48=\dfrac12[/tex]

There are 3 numbers less than 4 (1, 2 and 3)

[tex]\sf \implies Probability\:of\:landing\:on\:a\:number\:less\:than\:4=\dfrac38[/tex]

Therefore, the probability of landing of an even number and then on a number of less than 4 is:

[tex]\sf \implies Probability=\dfrac12 \times \dfrac38=\dfrac{3}{16}[/tex]

What is the length of this key to the nearest quarter inch?


3 inches

314 inches

312 inches

334 inches
Key laying horizontally with vertical markers indicating the left and right ends of the key.

Answers

the length of the key will be 3 inched long because it is laying horizontally

Use a net to find the surface area of the cylinder. Use 3.14 for pie

Answers

Answer:

62.83

nearest tenth 62.8

Simplify: 4/15+7/8-11/12​

Answers

Answer:

[tex]\frac{9}{40}[/tex]

Step-by-step explanation:

LCD: 120

[tex]\frac{4}{15} +\frac{7}{8} -\frac{11}{12}[/tex]

[tex]\frac{32}{120} +\frac{105}{120} -\frac{110}{120}[/tex]

[tex]\frac{27}{120}[/tex]

[tex]\frac{9}{40}[/tex]

Hope this helps!

Answer:

9/40

hope this helps.

What is 9n=1(98-2n) equal to? Id really appreciate if you could answer both though

Answers

N=32/3as a fraction alternative form is n=10.6


PLEASE HELP ME OUT AND PLEASE

Answers

Answer:

65⁰ because the opposite angles of parallelogram are equal...

1) A user must be at least 13 years old to set up a video-sharing account.
Let x be the age in years of a user who can set up an account.
Which inequality represents the situation?

Answers

Answer: x [tex]\geq[/tex] 13

Step-by-step explanation: quite simple actually, since the user must be AT LEAST 13 years old to set up the account, the equation would be X is greater than or equal to 13.

Hope this helps

Lilit and Sergio sold candles for a class trip. On the first day, Lilit sold 8 candles and Sergio sold 10 candles. For the next three days, both sold another 3 candles each day.PLEASE HELP

Answers

Answer:

Lilit- 17 candles

Sergio- 19 candles

Step-by-step explanation:

this is the most probable answer.

The original price is $125. The sale price is $81.25. How much was the discount as a percent?

Answers

Answer: 35%

Step-by-step explanation:

Start by subtracting the original price by the sale price.

125-81.25=43.75

Now divide that amount by the original price.

[tex]\frac{43.75}{125} =0.35[/tex]

Multiply that value by 100 for the answer

0.35×100=35

35%

Answer:

Discount Percent = 35.00 %

Step-by-step explanation:

125-81.25=43.75 actual discount

43.75/125 = 0.35 actual discount / original

0.35 as percentage = 35%  

You took a test and got 12 points on it. The next week, you retook it and got 25% more points than before. How many points did you get when you retook it?

Answers

Answer:

15 points

Step-by-step explanation:

12 divied by .25 =3

so there for it would be 15 points

Answer:

The answer is 15 points. Have a great day:)

If you can help me with this please and thank you

Answers

Answer:

1) im not sure

2) im not sure

3) 72 degrees

Step-by-step explanation:

Suppose there are 20 equally-sized marbles in a bag. Six marbles are blue, seven red, three of them orange, three of them black, and one green. If you choose a red marble, you win nothing. Selecting a blue marble will win you 25 cents. Selecting an orange marble will win you 50 cents, selecting a black marble will cost you a dollar, and if you choose the green one, you win three dollars.

Answers

Answer:

i dont know what youre trying to answer but if your trying to answer how much money can you get if you get all of the marbles you get $9

just blue- $1.50

just orange- $1.50

just black- $3

just green- $3

red=$0

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