Average Rate of Change Interval and Increasing and Decreasing Table

Find the average rate of change over the interval [-2 , 4].

Type answer as a fraction.

Find the average rate of change over the interval [-2 , 4].

Type answer as a fraction

What are the intervals of x where the function g is increasing at a decreasing rate?

• (-2,1)

• (-2,4)

• (1,4)

• (1,6)

The table shows the values for a function f at selected values of x. Which of the following claim and explanation statements best fit these data?

• f is the best fit model by linear function because the rate of change over consecutive equal-length input-value intervals is constant. The constant rate of change is -3.

• f is the best fit model by linear function because the rate of change over consecutive equal-length input-value intervals is linear.

• f is the best fit model by quadratic function because the rate of change over consecutive equal-length input-value intervals is constant.

• f is the best fit model by quadratic function because the rate of change over consecutive equal-length input-value intervals is linear

The table shows values for a function k at selected values of x. Which of the following claim and explanation statements best fit these data?

• k is the best modeled by a linear function because the rate of change over consecutive equal-length input-value intervals is constant

• k is the best modeled by a linear function because the rate of change over consecutive equal-length input-value intervals is linear

• k is the best modeled by a quadratic function because the rate of change over consecutive equal-length input-value intervals is constant

• k is the best modeled by a quadratic function because the rate of change over consecutive equal-length input-value intervals is linear. The rate of change is changing at a constant rate of -1

Information about the function g(x) is given in the table. The function g(x) is defined for all real numbers. Which of the following statements is guaranteed to be true about g(x)?

• g(x)

  has a relative maximum at

  x=-2.

  

• g(x)

  has a relative minimum at

  x=4.

• g(x)=0

  for some

  x

  in the interval

  [-2,4].

  

• The range of

  g(x) is (-∞, 11]

Luna, Anika, and Mia are studying for their math test. They come across a function whose values are given at selected 𝒙-values in the table below. They notice that the function’s concavity does not change. Can you help them determine if the function is concave up or concave down? Justify your answer.

• Concave up because the rate of change is increasing over equal‐length input‐value intervals.

• Concave down because the rate of change is increasing over equal‐length input‐value intervals.

• Concave down because the rate of change is decreasing over equal‐length input‐value intervals.

• Concave up because the rate of change is decreasing over equal‐length input‐value intervals.

The values of a function are given at selected 𝒙-values in the table below. The function’s concavity does not change. Determine if the function is concave up or concave down. Justify your answer.

• Concave up because the rate of change is decreasing over equal-length input-value intervals.

• Concave down because the rate of change is decreasing over equal-length input-value intervals.

• Concave down because the rate of change is increasing over equal-length input-value intervals.

• Concave up because the rate of change is increasing over equal-length input-value intervals.

Abigail, Aiden, and William are on a treasure hunt. They found a map with a strange equation h(x) = -7x + 5. They need to find the average rate of change of this function on -5 ≤ x ≤ 10 to unlock the next clue. Can you help them?

• -7

• 7

• different values

• 5

Benjamin, Maya, and Mia are studying quadratic functions. They come across a function 𝒈 and notice some interesting patterns. They find that the average rate of change is -6 on the interval 0 ≤ x ≤ 5. They also observe that the average rate of change is -2 on the interval 5 ≤ x ≤ 10. They are now curious to know what would be the average rate of change of 𝑔 on the interval 20 ≤ x ≤ 25. Can you help them figure it out?

• 2

• 6

• 10

• 14