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

$$f$$ is best modeled by a quadratic function because the average rate of change over each interval is linear.

$$f$$ is best modeled by a linear function because the average rate of change over each interval is linear.

$$f$$ is best modeled by a linear function because the average rate of change over each interval is constant.

$$f$$ is best modeled by a quadratic function because the average rate of change over each interval is constant.

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?

The graph of $$k$$ could be concave down because the average rates of change over consecutive equal-length input-value intervals are decreasing.

The graph of $$k$$ could be concave up because the average rates of change over consecutive equal-length input-value intervals are positive.

The graph of $$k$$ could be concave up because the average rates of change over consecutive equal-length input-value intervals are increasing.

The graph of $$k$$ could be concave down because the average rates of change over consecutive equal-length input-value intervals are negative.

The figure shows the graph of a function. Which of the following statements is correct?

the function is negative and increasing

the function is negative and decreasing

the function is positive and increasing

the function is positive and decreasing

The figure shows the graph of a function. Which of the following statements is correct?

the rate of change is positive is decreasing

the rate of change is positive and increasing

the rate of change is negative and increasing

the rate of change is negative and decreasing

The figure shows the graph of a function. Which of the following statements is correct?

the function is decreasing at a decreasing rate

the function is decreasing at a increasing rate

the function is increasing at a decreasing rate

the function is increasing at a increasing rate

Increasing Decreasing Intervals Quadratic

Authored by Anthony Clark

Mathematics

9th Grade

CCSS covered

Increasing Decreasing Intervals Quadratic

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MULTIPLE CHOICE QUESTION

1 min • 2 pts

For what intervals of x is f(x) positive?

x≤-1

x≥-1

-3<x<1

-3≤x≤1

What are the decreasing intervals?

MULTIPLE CHOICE QUESTION

1 min • 1 pt

What are the increasing intervals?

MULTIPLE CHOICE QUESTION

1 min • 1 pt

f(x) = 3x² + 5x - 9

UP and UP

DOWN and DOWN

UP and DOWN

DOWN and UP

MULTIPLE CHOICE QUESTION

1 min • 1 pt

f(x) = -3x² - 5x + 12

UP and UP

DOWN and DOWN

UP and DOWN

DOWN and UP

What is the end behavior?

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Increasing Decreasing Intervals Quadratic

For what intervals of x is f(x) positive?

What are the decreasing intervals?

What are the increasing intervals?

f(x) = 3x2 + 5x - 9

f(x) = -3x2 - 5x + 12

What is the end behavior?

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f(x) = 3x² + 5x - 9

f(x) = -3x² - 5x + 12