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Use the table to answer the question.

x y
0 −5
1 −9
2 −13
3 −17
Which of the following equations correctly describes the function in the table using function notation?



(1 point)
Responses

f(y)=−5x−4
f left parenthesis y right parenthesis equals negative 5 x minus 4

f(y)=−4x−5
f left parenthesis y right parenthesis equals negative 4 x minus 5

f(x)=−4x−5
f left parenthesis x right parenthesis equals negative 4 x minus 5

f(x)=−5x−4

f of x is equal to negative 5 x minus 4
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Use the image to answer the question.

Two side-by-side shaded ovals labeled x and y each display a list of values. Four arrows point from the values in the left oval, x, to the values in the right oval, y.

Which equation describes the function shown in the mapping diagram?

(1 point)
Responses

f(x)=12x−8
f left parenthesis x right parenthesis equals Start Fraction 1 over 2 End Fraction x minus 8

f(y)=12x−8
f left parenthesis y right parenthesis equals Start Fraction 1 over 2 End Fraction x minus 8

f(x)=8x−12
f left parenthesis x right parenthesis equals 8 x minus Start Fraction 1 over 2 End Fraction

f(y)=8x−12
f left parenthesis y right parenthesis equals 8 x minus Start Fraction 1 over 2 End Fraction
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Evaluate the function for the following input: f(x)=3−2x
. Which input generates the largest output when evaluating the function?(1 point)
Responses

f(5)
f left parenthesis 5 right parenthesis

f(0)
f left parenthesis 0 right parenthesis

f(2)
f left parenthesis 2 right parenthesis

f(3)

The function V(r)=10πr2
represents the volume of a cylinder that is 10 inches high with a radius of r. Which is the correct interpretation for the function notation V(3)=90π
?(1 point)
Responses

A radius of 3 gives the value 90.
A radius of 3 gives the value 90.

The volume of the cylinder is 3 when the radius is 90π
.
The volume of the cylinder is 3 when the radius is 90 pi .

A cylinder of 90π
is produced from a radius of 3.
A cylinder of 90 pi is produced from a radius of 3.

The volume of the cylinder is 90π
when the radius is 3.
The volume of the cylinder is 90 pi when the radius is 3.

onique is punting a football and the height the ball travels is a function of time. The function h(s)=−s2+10s+3
gives the height of the ball, h(s)
, given the number of seconds, s
, that the ball has been in the air. After flying through the air for 7.5 seconds, what is the height of the ball? Find h(7.5)
.(1 point)
Responses

24
24

134.25
134.25

21.75
21.75

21.5

1 answer

Let's break down each of your questions step by step.

  1. Function from the Table: The table shows a linear relationship between \( x \) and \( y \).

    If we examine the values:

    • At \( x = 0 \), \( y = -5 \)
    • At \( x = 1 \), \( y = -9 \)
    • At \( x = 2 \), \( y = -13 \)
    • At \( x = 3 \), \( y = -17 \)

    It appears that for each increase in \( x \) by 1, \( y \) decreases by 4. This suggests a linear function of the form: \[ y = -4x - 5 \] Rewriting in function notation gives: \( f(x) = -4x - 5 \)

    So, the correct response is: f(x) = -4x - 5.

  2. Mapping Diagram: Since the specific values from the mapping diagram are not provided, let’s analyze the equations given. If the diagram suggests that for each \( x \) there is a corresponding \( y \), we can determine how \( y \) is related to \( x \).

    From the options, if more context were provided, you would look for a linear equation given input-output pairs that show a clear relationship. Without the specifics, I cannot determine the correct option. However, the key is to find the equation that accurately reflects the transformation from \( x \) to \( y \) in the diagram.

  3. Evaluate the Function \( f(x) = 3 - 2x \): We need to evaluate \( f(x) \) at the provided inputs:

    • \( f(5) = 3 - 2(5) = 3 - 10 = -7 \)
    • \( f(0) = 3 - 2(0) = 3 - 0 = 3 \)
    • \( f(2) = 3 - 2(2) = 3 - 4 = -1 \)
    • \( f(3) = 3 - 2(3) = 3 - 6 = -3 \)

    The largest output is \( f(0) = 3 \).

    So, the correct response is: f(0).

  4. Interpretation of the Cylinder Volume Function: The function \( V(r) = 10\pi r^2 \) gives the volume of a cylinder with height 10 and radius \( r \). The notation \( V(3) = 90\pi \) means that when the radius is 3, the resulting volume is \( 90\pi \).

    Thus, the correct interpretation is: The volume of the cylinder is \( 90\pi \) when the radius is 3.

  5. Height of the Football: Now we need to calculate \( h(7.5) \): \[ h(7.5) = - (7.5)^2 + 10(7.5) + 3 \] Calculate each part: \[

    • (7.5)^2 = - 56.25 \] \[ 10(7.5) = 75 \] Now sum everything: \[ h(7.5) = -56.25 + 75 + 3 = -56.25 + 78 = 21.75 \]

    Therefore, the correct response is: 21.75.

If you have specific numbers or details for the questions involving the mapping diagram, please provide those for more accurate assistance!