Question 1 A) 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)=−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(y)=−5x−4 f left parenthesis y right parenthesis equals negative 5 x minus 4 f(x)=−5x−4 f of x is equal to negative 5 x minus 4 Question 2 A) Use the image to answer the question. Which equation describes the function shown in the mapping diagram? (1 point) Responses f(y)=12x−8 f left parenthesis y right parenthesis equals Start Fraction 1 over 2 End Fraction x minus 8 f(x)=12x−8 f left parenthesis x right parenthesis equals Start Fraction 1 over 2 End Fraction x minus 8 f(y)=8x−12 f left parenthesis y right parenthesis equals 8 x minus Start Fraction 1 over 2 End Fraction f(x)=8x−12 f left parenthesis x right parenthesis equals 8 x minus Start Fraction 1 over 2 End Fraction Question 3 A)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(3) f left parenthesis 3 right parenthesis f(2) f left parenthesis 2 right parenthesis f(0) f left parenthesis 0 right parenthesis f(5) f left parenthesis 5 right parenthesis Question 4 A)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 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. 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. Question 5 A)Monique 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 21.75 21.75 24 24 21.5 21.5 134.25 134.25

Let's answer the questions one by one.

Question 1

The data given is:

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

We can observe that as \( x \) increases by 1, \( y \) decreases by 4. This indicates a linear relationship described by the equation: \[ y = -4x - 5 \] Thus, in function notation, it can be written as: \[ f(x) = -4x - 5 \] Correct answer: \( f(x) = -4x - 5 \)

Question 2

We need to check the mapping diagram to determine the function. Since I do not have access to the image, I can't analyze the specific mapping. However, based on the provided responses, if \( f(x) = \frac{1}{2}x - 8 \), choose that response. If it's something else based on the diagram you see, select accordingly.

Question 3

For the function \( f(x) = 3 - 2x \), let's evaluate it for the provided inputs:

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

Thus, the largest output is \( f(0) = 3 \). Correct answer: \( f(0) \)

Question 4

The function \( V(r) = 10\pi r^2 \) represents the volume of a cylinder. When \( r = 3 \): \[ V(3) = 10\pi(3^2) = 10\pi \times 9 = 90\pi \]

Thus, the interpretation is that the volume of the cylinder is \( 90\pi \) when the radius is \( 3 \). Correct answer: The volume of the cylinder is 90π when the radius is 3.

Question 5

Now we need to evaluate \( h(7.5) \) for the function \( h(s) = -s^2 + 10s + 3 \): \[ h(7.5) = - (7.5)^2 + 10(7.5) + 3 = -56.25 + 75 + 3 = 21.75 \] Correct answer: \( 21.75 \)

If you have any more questions or further clarification is needed, feel free to ask!

Thank you for providing the data for Question 2. Based on the mapping you provided, we can determine the relationship between \( x \) and \( y \):

• When \( x = 0, y = -8 \)
• When \( x = 1, y = -7.5 \)
• When \( x = 2, y = -7 \)
• When \( x = 3, y = -6.5 \)

We can observe the pattern in the changes:

• From \( 0 \) to \( 1 \): \( -8 \) to \( -7.5 \) (increase of \( 0.5 \))
• From \( 1 \) to \( 2 \): \( -7.5 \) to \( -7 \) (increase of \( 0.5 \))
• From \( 2 \) to \( 3 \): \( -7 \) to \( -6.5 \) (increase of \( 0.5 \))

This indicates that for every increase of \( 1 \) in \( x \), \( y \) increases by \( 0.5 \). Therefore, we can express this relationship with the linear equation: \[ y = 0.5x - 8 \]

In function notation, this is written as: \[ f(x) = 0.5x - 8 \]

Looking at the response options provided, if your options included \( f(x) = \frac{1}{2}x - 8 \), that would be the correct answer.

Correct answer: \( f(x) = \frac{1}{2}x - 8 \)

Thank you for clarifying the values from the mapping diagram. Let’s summarize the information provided:

• When \( x = 0, y = -8 \)
• When \( x = 1, y = -7.5 \) (or \(-7 \frac{1}{2}\))
• When \( x = 2, y = -7 \)
• When \( x = 3, y = -6.5 \) (or \(-6 \frac{1}{2}\))

To find the equation that describes the function shown in the mapping diagram, we need to examine the changes in \( x \) and \( y \):

1. From \( (0, -8) \) to \( (1, -7.5) \): an increase of \( 0.5 \) in \( y \)
2. From \( (1, -7.5) \) to \( (2, -7) \): another increase of \( 0.5 \) in \( y \)
3. From \( (2, -7) \) to \( (3, -6.5) \): yet another increase of \( 0.5 \) in \( y \)

The relationship appears linear and can be written in the form: \[ y = mx + b \] Where \( m \) is the slope. We see that the slope (\( m \)) is \( 0.5 \) (or \(\frac{1}{2}\)), and we can calculate the y-intercept (\( b \)) by using one of the points:

Using the point \( (0, -8) \): \[ y = 0.5x - 8 \]

Therefore, in function notation, the equation becomes: \[ f(x) = 0.5x - 8 \]

From the options provided in your original question, if there is one that states \( f(x) = \frac{1}{2}x - 8\), that is the correct response.

Correct Answer: \( f(x) = \frac{1}{2}x - 8 \)