Question

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)=8x−12 f left parenthesis y right parenthesis equals 8 x minus Start Fraction 1 over 2 End Fraction 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 THE MAP : (0,-8)(1,-7 1/2) (2,-7) (3,-61/2)

Answer 1

To determine the equation that describes the function based on the given mapping diagram points \((0, -8)\), \((1, -7.5)\), \((2, -7)\), and \((3, -6.5)\), we need to analyze these points and find a linear equation that fits them.

The points correspond to the following values:

• \( f(0) = -8 \)
• \( f(1) = -7.5 \)
• \( f(2) = -7 \)
• \( f(3) = -6.5 \)

Let's determine the slope (m) between two consecutive points, for instance between \((0, -8)\) and \((1, -7.5)\):

\[ m = \frac{-7.5 - (-8)}{1 - 0} = \frac{0.5}{1} = 0.5 \]

Thus, the slope of the function is \(0.5\).

Next, we can write the equation in point-slope form \(y - y_1 = m(x - x_1)\). Using the point \((0, -8)\):

\[ f(x) - (-8) = 0.5(x - 0) \] \[ f(x) + 8 = 0.5x \] \[ f(x) = 0.5x - 8 \]

Now we can match this with the given options. The function \(f(x) = \frac{1}{2}x - 8\) matches our derived equation.

Thus, the equation that describes the function is:

\[ f(x) = \frac{1}{2}x - 8 \]

So the correct response is:

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

Answer 2

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(0) f left parenthesis 0 right parenthesis f(5) f left parenthesis 5 right parenthesis f(3) f left parenthesis 3 right parenthesis f(2)

Answer 3

To find which input generates the largest output for the function \( f(x) = 3 - 2x \), we need to evaluate the function at each of the given inputs: \(0\), \(5\), \(3\), and \(2\).

1. Evaluate \( f(0) \): \[ f(0) = 3 - 2(0) = 3 - 0 = 3 \]

2. Evaluate \( f(2) \): \[ f(2) = 3 - 2(2) = 3 - 4 = -1 \]

3. Evaluate \( f(3) \): \[ f(3) = 3 - 2(3) = 3 - 6 = -3 \]

4. Evaluate \( f(5) \): \[ f(5) = 3 - 2(5) = 3 - 10 = -7 \]

Now we summarize the outputs:

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

Among these values, the largest output is from \( f(0) \), which is \(3\).

Thus, the input that generates the largest output is:

\( f(0) \).

Answer 4

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. 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 3 when the radius is 90π.

Answer 5

The function \( V(r) = 10\pi r^2 \) gives the volume of a cylinder with a height of 10 inches and a radius \( r \). When we evaluate this function at \( r = 3 \), we find:

\[ V(3) = 10\pi(3^2) = 10\pi(9) = 90\pi \]

The interpretation of the function notation \( V(3) = 90\pi \) indicates that when the radius of the cylinder is 3 inches, the volume of the cylinder is \( 90\pi \) cubic inches.

Thus, the correct interpretation of the function notation \( V(3) = 90\pi \) is:

The volume of the cylinder is \( 90\pi \) when the radius is 3.