Quiz on Lessons 1.3-1.4

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.

Anika, Grace, and David are playing a game of 'Guess the Function'. They have a table that gives values of a mysterious function ℎ for selected values of 𝑥.

They discovered that if the function f is linear, they can predict the next value. Can you help them guess what the value of f(32) would be if the function is indeed linear?

• -3

• 36

• 92

• -92

• -7

• 7

• different values

• 5

• -9

• 9

• -27/7

• -1/3

• 2

• 6

• 10

• 14

What is the rate of change of the average rates of change for each function over consecutive equal-length intervals?

y = -0.5 x

• -0.5

• 0

• 0.5

• 1

• Leading Coefficient: -10

  Degree: 3

• Leading Coefficient: -3

  Degree: 4

• Leading Coefficient: 4

  Degree: -3

• Leading Coefficient: -10

  Degree: 3

• Leading Coefficient: -3

  Degree: 5

• Leading Coefficient: -24

  Degree: 5

• Leading Coefficient: -24

  Degree: 3

• Leading Coefficient: -6

  Degree: 5