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 average rate of change of $$f$$ over consecutive equal-length input-value intervals can be described as line with a negative slope, which of the following statements about the graph of $$f$$ must be true?

the graph of $$f$$ could be a quadratic with an decreasing rate of change

the graph of $$f$$ could be a line with a positive slope

the graph of $$f$$ could be a line with a negative slope

the graph of $$f$$ could be a quadratic with an increasing rate of change

Increasing and Decreasing Intervals Quadratic

Authored by Anthony Clark

Mathematics

11th Grade

CCSS covered

Used 1+ times

Increasing and Decreasing Intervals Quadratic

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MULTIPLE CHOICE QUESTION

1 min • 1 pt

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

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Increasing and Decreasing Intervals Quadratic

What are the decreasing intervals?

What are the increasing intervals?

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

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

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f(x) = 3x² + 5x - 9

f(x) = -3x² - 5x + 12