Algebra 1B Unit 2 Lesson 10

Examine the following graph of the linear function f(x)=2x+1 and the quadratic function g(x)=−1/16(x+3)^2 +6. https://assets.learnosity.com/organisations/625/asset/media/1155349 Which statements about the functions are true? There is more than one correct answer. Select all correct answers.

- Over the interval −8≤x≤−3, the average rate of change of g(x) is slower than the average rate of change of f(x). - Over the interval 4≤x≤6, the average rate of change of g(x) is slower than the average rate of change of f(x). - Over the interval −8≤x≤−7, the average rate of change of g(x) is slower than the average rate of change of f(x).

Compare the two functions, f(x)=−4x+12 and g(x)=(1/4)^x +8, in the following graph. https://assets.learnosity.com/organisations/625/asset/media/1155351 Which statements about the functions are true? There is more than one correct answer. Select all correct answers.

- The average rate of change for f(x) over the interval 2 to 3 is faster than the average rate of change for g(x). - The average rate of change for g(x) over the interval −2 to −1 is faster than the average rate of change for f(x). - The average rate of change for g(x) over the interval −1 to 0 is −3. - The average rate of change for f(x) over the interval −1 to 0 is −4.

Compare the two functions in the following graph. https://assets.learnosity.com/organisations/625/asset/media/1155354 Which statements about the functions are true? There is more than one correct answer. Select all correct answers.

- The average rate of change of f(x) is faster than the average rate of change of g(x) over the interval 1≤x≤6. - The average rate of change of g(x) is faster than the average rate of change of f(x) from −2 to 0.

A linear function is represented by the values in the following input-output table. (-2,-2) (0,-3) (2,-4) (4,-5) What is the rate of change of the function?

-1/2

A rocket is launched into the air. The height h(t), in yards, of the rocket is a function of time, t, in seconds, as shown in the following table. (0,0) (1,20) (2,28) (3,33) (4,28) (5,20) (6,0) What is the rocket's average rate of change from 3≤t≤6 in yards/second? Enter your answer as a number, like this: 42

-11

The decrease in the worth of Kenzie's car can be represented by the function m(t)=23,000(0.97)t, where t is the time in years, and m is the car's value in dollars. What is the average rate of change of the car's value in dollars per year (rounded to the nearest dollar) during the first 4 years Kenzie owns it?

-660

Using the formula m=f(x^2)−f(x^1)x^2−x^1, what is the rate of change for the linear function that contains the points (−3,2) and (1,10)?

2

Examine the following graph of a nonlinear function. https://assets.learnosity.com/organisations/625/asset/media/1060115 What is the average rate of change over the interval 1≤x≤3? Enter your answer as a number, like this: 42

3

James is contemplating an investment opportunity represented by the function A(t)=P(1.06)t, where P is the initial amount of the investment, and t is the time in years. If James invests $5000, what is the average rate of change in dollars per year (rounded to the nearest dollar) between years 15 and 20? Enter your answer as a number, like this: 42

811

Which option can be modeled by a linear function.

Adding $2 to a piggy bank each week.

Examine the following graph. https://assets.learnosity.com/organisations/625/asset/media/1155344 What is the rate of change of the graphed function?

Every year, the height increases by 5 inches, so the rate of change is 5 inches/year.

Use the following graph of two functions to answer the question. https://assets.learnosity.com/organisations/625/asset/media/1155355 Which statement about the functions is true?

The average rate of change of f(x) is faster than the average rate of change of g(x) from −3 to −2.