Question
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(x)=−5x−4
f of x is equal to negative 5 x minus 4
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(y)=−4x−5
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(x)=−5x−4
f of x is equal to negative 5 x minus 4
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(y)=−4x−5
Answers
Answer
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)=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
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
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)=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
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
Answer
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(3)
f left parenthesis 3 right parenthesis
f(2)
f left parenthesis 2 right parenthesis
f(5)
. Which input generates the largest output when evaluating the function?(1 point)
Responses
f(0)
f left parenthesis 0 right parenthesis
f(3)
f left parenthesis 3 right parenthesis
f(2)
f left parenthesis 2 right parenthesis
f(5)
Answer
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 cylinder of 90π
is produced from a radius of 3.
A cylinder of 90 pi is produced from a radius of 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 .
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 cylinder of 90π
is produced from a radius of 3.
A cylinder of 90 pi is produced from a radius of 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 .
Answer
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
21.5
21.5
134.25
134.25
21.75
21.75
24
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
21.5
21.5
134.25
134.25
21.75
21.75
24
Answered by
GPT-4o mini
To find the correct equation that describes the function in the table, we can analyze the given points to determine the relationship between x and y.
The provided points are:
- When \( x = 0 \), \( y = -5 \)
- When \( x = 1 \), \( y = -9 \)
- When \( x = 2 \), \( y = -13 \)
- When \( x = 3 \), \( y = -17 \)
The values of y decrease by 4 for each increment of 1 in x.
We can look for a linear relationship of the form \( y = mx + b \).
Given that the slope (m) is -4, we can calculate the y-intercept (b) when \( x = 0 \):
- For \( x = 0 \): \( y = -5 \) implies \( b = -5 \).
So, the equation in the form of \( y = mx + b \) is:
\[
y = -4x - 5
\]
Since the prompt is asking for function notation, we will rewrite this as:
\[
f(x) = -4x - 5
\]
**Thus, the correct response is:**
f(x) = −4x − 5
(f of x is equal to negative 4 x minus 5)
The provided points are:
- When \( x = 0 \), \( y = -5 \)
- When \( x = 1 \), \( y = -9 \)
- When \( x = 2 \), \( y = -13 \)
- When \( x = 3 \), \( y = -17 \)
The values of y decrease by 4 for each increment of 1 in x.
We can look for a linear relationship of the form \( y = mx + b \).
Given that the slope (m) is -4, we can calculate the y-intercept (b) when \( x = 0 \):
- For \( x = 0 \): \( y = -5 \) implies \( b = -5 \).
So, the equation in the form of \( y = mx + b \) is:
\[
y = -4x - 5
\]
Since the prompt is asking for function notation, we will rewrite this as:
\[
f(x) = -4x - 5
\]
**Thus, the correct response is:**
f(x) = −4x − 5
(f of x is equal to negative 4 x minus 5)
Answered by
GPT-4o mini
To solve the problem, we need to analyze what the mapping diagram indicates about the relationship between the values in set \( x \) and the values in set \( y \) as illustrated by the arrows.
Without seeing the specific values in the ovals or the directions of the arrows, I can guide you on how to figure out which equation describes the function.
1. **Understanding Function Notation**: A function can be represented in the form \( f(x) \), where \( x \) is the input from the left oval, and \( f(x) \) is the output in the right oval.
2. **Finding the Relationship**:
- Check how the values in \( x \) transform into values in \( y \) using the mappings (arrows).
- If we have specific numbers, identify whether they show a consistent pattern. For example, do the outputs increase by a certain factor or decrease by a certain amount?
- Calculate any differences, ratios, or other relationships that emerge.
3. **Choosing the Correct Equation**:
- The functions specified in each option need to be evaluated based on the transformations you recognize.
- An equation like \( f(x) = 8x - 12 \) implies that for every input \( x \), you multiply it by 8 and then subtract 12 to find the corresponding \( y \).
Assuming you've done that analysis:
- If there’s a consistent relationship where you can express \( y \) in terms of \( x \) like those options show, find which one matches your analysis.
- If the relationship shows doubling, halving, or adding/subtracting values, it will give you insight into which equation corresponds to the mapping.
If you provide specific values from the diagram, I can help you further analyze and correctly identify the function that describes the relationship based on those values. But based on the choices:
- The correct form should be \( f(x) \) if it's mapping \( x \) to \( y\).
If you verify the mappings you observed, you’ll be able to choose the equation that correctly describes the transformation.
Without seeing the specific values in the ovals or the directions of the arrows, I can guide you on how to figure out which equation describes the function.
1. **Understanding Function Notation**: A function can be represented in the form \( f(x) \), where \( x \) is the input from the left oval, and \( f(x) \) is the output in the right oval.
2. **Finding the Relationship**:
- Check how the values in \( x \) transform into values in \( y \) using the mappings (arrows).
- If we have specific numbers, identify whether they show a consistent pattern. For example, do the outputs increase by a certain factor or decrease by a certain amount?
- Calculate any differences, ratios, or other relationships that emerge.
3. **Choosing the Correct Equation**:
- The functions specified in each option need to be evaluated based on the transformations you recognize.
- An equation like \( f(x) = 8x - 12 \) implies that for every input \( x \), you multiply it by 8 and then subtract 12 to find the corresponding \( y \).
Assuming you've done that analysis:
- If there’s a consistent relationship where you can express \( y \) in terms of \( x \) like those options show, find which one matches your analysis.
- If the relationship shows doubling, halving, or adding/subtracting values, it will give you insight into which equation corresponds to the mapping.
If you provide specific values from the diagram, I can help you further analyze and correctly identify the function that describes the relationship based on those values. But based on the choices:
- The correct form should be \( f(x) \) if it's mapping \( x \) to \( y\).
If you verify the mappings you observed, you’ll be able to choose the equation that correctly describes the transformation.
Answered by
GPT-4o mini
To find out which input generates the largest output for the function \( f(x) = 3 - 2x \), we'll evaluate the function for each of the given inputs: \( 0, 2, 3, \) and \( 5 \).
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 let's summarize the output values:
- \( f(0) = 3 \)
- \( f(2) = -1 \)
- \( f(3) = -3 \)
- \( f(5) = -7 \)
The largest output value is from \( f(0) \), which equals \( 3 \).
**Therefore, the input that generates the largest output is:**
- \( f(0) \) (f of 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 let's summarize the output values:
- \( f(0) = 3 \)
- \( f(2) = -1 \)
- \( f(3) = -3 \)
- \( f(5) = -7 \)
The largest output value is from \( f(0) \), which equals \( 3 \).
**Therefore, the input that generates the largest output is:**
- \( f(0) \) (f of 0)
Answered by
GPT-4o mini
To interpret the function notation \( V(3) = 90\pi \) in the context of the volume of a cylinder, let’s break down the meaning of \( V(r) \):
- The function \( V(r) \) computes the volume of a cylinder with height 10 inches and radius \( r \).
- Therefore, \( V(3) \) indicates that we are evaluating the volume of a cylinder with a radius of 3 inches.
Given that \( V(3) = 90\pi \), this means that when the radius is 3 inches, the resulting volume of the cylinder is \( 90\pi \) cubic inches.
Now, let’s look at the options:
1. **The volume of the cylinder is 90π when the radius is 3.**
2. **A cylinder of 90π is produced from a radius of 3.**
3. **A radius of 3 gives the value 90.**
4. **The volume of the cylinder is 3 when the radius is 90π.**
The most accurate interpretation from the given choices is:
**The volume of the cylinder is 90π when the radius is 3.**
This option correctly reflects the definition of the function and the specific evaluation given in the function notation.
- The function \( V(r) \) computes the volume of a cylinder with height 10 inches and radius \( r \).
- Therefore, \( V(3) \) indicates that we are evaluating the volume of a cylinder with a radius of 3 inches.
Given that \( V(3) = 90\pi \), this means that when the radius is 3 inches, the resulting volume of the cylinder is \( 90\pi \) cubic inches.
Now, let’s look at the options:
1. **The volume of the cylinder is 90π when the radius is 3.**
2. **A cylinder of 90π is produced from a radius of 3.**
3. **A radius of 3 gives the value 90.**
4. **The volume of the cylinder is 3 when the radius is 90π.**
The most accurate interpretation from the given choices is:
**The volume of the cylinder is 90π when the radius is 3.**
This option correctly reflects the definition of the function and the specific evaluation given in the function notation.
Answered by
GPT-4o mini
To find the height of the football after 7.5 seconds using the function \( h(s) = -s^2 + 10s + 3 \), we need to evaluate \( h(7.5) \).
Substituting \( s = 7.5 \) into the function:
\[
h(7.5) = -(7.5)^2 + 10(7.5) + 3
\]
Now let's calculate each term step-by-step:
1. Calculate \( (7.5)^2 \):
\[
(7.5)^2 = 56.25
\]
2. Calculate \( 10(7.5) \):
\[
10(7.5) = 75
\]
3. Putting it all together in the function:
\[
h(7.5) = -56.25 + 75 + 3
\]
4. Simplifying:
\[
h(7.5) = -56.25 + 75 = 18.75
\]
\[
h(7.5) = 18.75 + 3 = 21.75
\]
So, the height of the ball after 7.5 seconds is:
**21.75**
Thus, the correct response is:
**21.75**
Substituting \( s = 7.5 \) into the function:
\[
h(7.5) = -(7.5)^2 + 10(7.5) + 3
\]
Now let's calculate each term step-by-step:
1. Calculate \( (7.5)^2 \):
\[
(7.5)^2 = 56.25
\]
2. Calculate \( 10(7.5) \):
\[
10(7.5) = 75
\]
3. Putting it all together in the function:
\[
h(7.5) = -56.25 + 75 + 3
\]
4. Simplifying:
\[
h(7.5) = -56.25 + 75 = 18.75
\]
\[
h(7.5) = 18.75 + 3 = 21.75
\]
So, the height of the ball after 7.5 seconds is:
**21.75**
Thus, the correct response is:
**21.75**
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.