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

9 answers

To determine which equation correctly describes the function from the table, we first need to observe the relationship between \(x\) and \(y\).

The given points are:

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

To identify the function, let's look at the differences in \(y\) as \(x\) increases:

  • From \(x = 0\) to \(x = 1\): \(-9 - (-5) = -4\)
  • From \(x = 1\) to \(x = 2\): \(-13 - (-9) = -4\)
  • From \(x = 2\) to \(x = 3\): \(-17 - (-13) = -4\)

The \(y\) values decrease consistently by 4 as \(x\) increases by 1, suggesting a linear relationship. The slope \(m\) is \(-4\).

Next, we can use the slope-intercept form of the line, \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

Using the point \( (0, -5) \):

  • The slope \(m = -4\)
  • The y-intercept \(b = -5\)

Thus, the equation that describes the relationship is: \[ y = -4x - 5 \]

Now, we can express this in function notation: \[ f(x) = -4x - 5 \]

The correct answer from the provided responses is: f(x) = -4x - 5.

Use the image to answer the 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 f left parenthesis x right parenthesis equals 8 x minus Start Fraction 1 over 2 End Fraction Skip to navigation

To identify which equation describes the function shown in the mapping diagram, we can use the general characteristics of functions. Unfortunately, without an image to review, I cannot analyze specific values or graphical representations.

However, I can guide you through how to determine the correct function based on the typical properties we look for in these types of problems:

  1. Determine the Function Type: If the mapping diagram shows a linear relationship, the functions will typically either be linear functions in the form of \(f(x) = mx + b\) or a transformation of the input \(x\) (like scaling or translating).

  2. Check for Increasing/Decreasing Characteristics: The slope (\(m\)) will tell you if the function is increasing (positive slope) or decreasing (negative slope).

  3. Evaluate the Outputs: If possible, verify the corresponding outputs for specific inputs in the diagrams with the given equations. Substituting a value of \(x\) into each of the answer choices will yield corresponding outputs which you can compare to what is shown in the mapping.

  4. Terms Analysis: Look for constants in option responses to see if they match the patterns you observe.

Without the values from the image, I can't specify which exact equation is correct. However, utilizing the process above, you can analyze which equation matches the mapping diagram’s tendencies.

If you can describe specific values or characteristics from the diagram, I may be able to help more directly!

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

To determine which input generates the largest output for the function \( f(x) = 3 - 2x \), we will evaluate the function at 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 we summarize the outputs:

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

The largest output occurs at \( f(0) = 3 \).

Therefore, the input that generates the largest output is: \[ \boxed{f(0)} \]

The function V(r)=10πr^2 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 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. 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 .

To interpret the function notation \( V(3) = 90\pi \) correctly, we need to understand what \( V(r) \) represents in this context.

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

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

This calculation indicates that when the radius of the cylinder is 3 inches, the volume of the cylinder is \( 90\pi \) cubic inches.

Based on this understanding, the correct interpretation of \( V(3) = 90\pi \) is:

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

So the appropriate response is: \[ \boxed{\text{The volume of the cylinder is } 90\pi \text{ when the radius is } 3.} \]

Monique is punting a football and the height the ball travels is a function of time. The function h(s)=−s^2+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

To find the height of the football after 7.5 seconds using the function \( h(s) = -s^2 + 10s + 3 \), we need to substitute \( s = 7.5 \) into the function and calculate \( h(7.5) \).

Calculation:

  1. Substitute \( s = 7.5 \) into the function: \[ h(7.5) = -(7.5)^2 + 10(7.5) + 3 \]

  2. Calculate \( (7.5)^2 \): \[ (7.5)^2 = 56.25 \]

  3. Calculate \( 10(7.5) \): \[ 10(7.5) = 75 \]

  4. Substitute these values into the equation: \[ h(7.5) = -56.25 + 75 + 3 \]

  5. Combine the terms: \[ h(7.5) = -56.25 + 75 + 3 = -56.25 + 78 = 21.75 \]

Thus, the height of the ball after 7.5 seconds is:

\[ \boxed{21.75} \]