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)
Answers
GPT-4o mini
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:
\( f(x) = \frac{1}{2}x - 8 \)
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:
\( f(x) = \frac{1}{2}x - 8 \)
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)
GPT-4o mini
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:
**\( f(0) \)**.
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:
**\( f(0) \)**.
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.
GPT-4o mini
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.**
\[
V(3) = 10\pi(3^2) = 10\pi(9) = 90\pi
\]
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.**