Comparing Exponential, Linear, and Quadratic…

1

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What is the minimum y -value after which the exponential function will always be greater than the linear function?

A

y is equal to 5

B

y is equal to 4

C

y is equal to 3

D

y is equal to 1

2

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Which statement best describes the growth rates of the functions?

A

The exponential function grows faster than the quadratic function over only one interval; 2 is less than x comma x is less than or equal to 3 .

B

The exponential function grows faster than the quadratic function over two intervals; 2 is less than x comma x is less than or equal to 4 .

C

The exponential function grows faster than the quadratic function over the entire interval; 0 is less than x comma x is less than or equal to 4 .

D

The quadratic function grows faster than the exponential function over the entire interval; 0 is less than x comma x is less than or equal to 4 .

3

From x is equal to 0 to x is equal to 2 , which of the following best describes the growth of the two functions?

A

y is equal to 5 x grows slower than y is equal to 5 to the x th power .

B

y is equal to 5 x grows faster than y is equal to 5 to the x th power .

C

y is equal to 5 to the x th power grows over a different interval than y is equal to 5 x .

D

y is equal to 5 to the x th power grows at the same rate as y is equal to 5 x .

4

Which statement is true?

A

The growth rate of the exponential function exceeds the growth rate of the linear function for negative 1 is less than or equal to x comma x is less than or equal to 1 .

B

The growth rate of the exponential function exceeds the growth rate of the linear function for negative 1 is less than or equal to x comma x is less than or equal to 3 .

C

The growth rate of the exponential function exceeds the growth rate of the linear function for 1 is less than or equal to x comma x is less than or equal to 3 .

D

The growth rate of the exponential function exceeds the growth rate of the linear function for 0 is less than or equal to x comma x is less than or equal to 3 .

5

Considering only the domain shown on the graph, over which interval is the value of the exponential function greater than the value of the quadratic function?

A

1 is less than x comma x is less than or equal to 2 point 5

B

negative 0 point 5 is less than or equal to x comma x is less than 1

C

negative 2 point 5 is less than or equal to x comma x is less than or equal to negative 0 point 7 5

D

1 is less than x comma x is less than or equal to 1 point 5

6

What is the minimum y -value after which the exponential function will always be greater than the linear function?

A

y is equal to 4

B

y is equal to 3

C

y is equal to 1

D

y is equal to 2

7

For which pair of functions is the exponential consistently growing at a faster rate than the quadratic over the interval 0 is less than or equal to x comma x is less than or equal to 5 ?

A

Image with description On a coordinate plane, the x axis lists negative 1 to 5 by 1, and the y axis lists negative 2 to 8 by 1. The graph has two smooth curves. The first smooth curve originates below the negative direction of the x axis, goes through (0 comma 0), and moves further up. The second smooth curve is a parabola that opens up and has a vertex at the origin. It goes through (1 comma 3) and moves up. Both curves touch each other at the origin.

B

Image with description On a coordinate plane, the x axis lists negative 1 to 5 by 1 unit. The y axis lists negative 2 to 8 by 1 unit. The parabola opens up, has vertex at the origin, and passes through (negative 1 comma 4) and (1 comma 4). The curve goes through (0 comma 1), (1 comma 2), (2 comma 4), and (3 comma 8).

C

Image with description On a coordinate plane, the x axis lists negative 1 to 5 by 1, and the y axis lists negative 2 to 8 by 1. The graph has two smooth curves. The first smooth curve originates from the negative direction of the x axis, intersects the y axis at (0 comma 1), goes through (1 comma 4), and moves up. The second smooth curve is a parabola that opens up and has a vertex at the origin. It goes through (2, 2) and moves up.

D

Image with description On a coordinate plane, the x axis lists negative 1 to 5 by 1 unit. The y axis lists negative 2 to 8 by 1 unit. The parabola opens up, has vertex at the origin, and passes through (negative 1 comma 2) and (1 comma 2). The curve goes through (0 comma 1), (1 comma 2), (2 comma 4), and (3 comma 8).

8

For which pair of functions is the exponential consistently growing at a faster rate than the quadratic over the interval 0 is less than or equal to x comma x is less than or equal to 5 ?

A

Image with description On a coordinate plane, the x axis lists negative 1 to 5 by 1 unit. The y axis lists negative 2 to 8 by 1 unit. The parabola opens up, has vertex at the origin, and passes through (negative 1 comma 2) and (1 comma 2). The curve goes through (0 comma 1), (1 comma 2), (2 comma 4), and (3 comma 8).

B

Image with description On a coordinate plane, the x axis lists negative 1 to 5 by 1 unit. The y axis lists negative 2 to 8 by 1 unit. The parabola opens up, has vertex at the origin, and passes through (negative 1 comma 4) and (1 comma 4). The curve goes through (0 comma 1), (1 comma 2), (2 comma 4), and (3 comma 8).

C

Image with description On a coordinate plane, the x axis lists negative 1 to 5 by 1 unit. The y axis lists negative 2 to 8 by 1 unit. The parabola opens up, has vertex at the origin, and passes through (2 comma 2) and (4 comma 8). The curve goes through (0 comma 1) and (1 comma 4).

D

Image with description On a coordinate plane, the x axis ranges from negative 1 to 5 with an interval of 1 unit. The y axis ranges from negative 2 to 8 with in interval of 1 unit. The parabola opens up, has vertex at the origin, and passes through (negative 1 comma 3) and (1 comma 3). The curve goes through the origin, (1 comma 1), (2 comma 3), and (3 comma 7).

9

Over which interval does the growth rate of the exponential function continue to exceed the growth rate of the linear function?

A

x is equal to 0 to x is equal to 1 point 7 9

B

x is equal to 0 point 3 8 to x is equal to 1 point 7 9

C

x is equal to 0 to x is equal to 3

D

x is equal to 1 point 7 9 to x is equal to 3

10

Over which interval does the growth rate of the exponential function exceed the growth rate of the linear function?

A

1 is less than or equal to x comma x is less than or equal to 2

B

x is less than 1

C

x is greater than 2

D

0 is less than or equal to x comma x is less than or equal to 1

11

What is the minimum y -value after which the exponential function will always be greater than the linear function?

A

y is equal to 2

B

y is equal to 3

C

y is equal to 1

D

y is equal to 4

12

What is the minimum y -value after which the exponential function will always be greater than the linear function?

A

y is equal to 4

B

y is equal to 3

C

y is equal to 1

D

y is equal to 5

13

From x is equal to 0 to x is equal to 2 , which of the following best describes the growth of the two functions?

A

y is equal to 5 to the x th power grows at the same rate as y is equal to 5 x .

B

y is equal to 5 x grows faster than y is equal to 5 to the x th power .

C

y is equal to 5 x grows slower than y is equal to 5 to the x th power .

D

y is equal to 5 to the x th power grows over a different interval than y is equal to 5 x .

14

For which pair of functions is the exponential consistently growing at a faster rate than the quadratic over the interval 0 is less than or equal to x comma x is less than or equal to 5 ?

A

Image with description On a coordinate plane, the x axis lists negative 1 to 5 by 1, and the y axis lists negative 2 to 8 by 1. The graph has two smooth curves. The first smooth curve originates from the negative direction of the x axis, intersects the y axis at (0 comma 1), goes through (1 comma 4), and moves up. The second smooth curve is a parabola that opens up and has a vertex at the origin. It goes through (2, 2) and moves up.

B

Image with description On a coordinate plane, the x axis lists negative 1 to 5 by 1 unit. The y axis lists negative 2 to 8 by 1 unit. The parabola opens up, has vertex at the origin, and passes through (negative 1 comma 4) and (1 comma 4). The curve goes through (0 comma 1), (1 comma 2), (2 comma 4), and (3 comma 8).

C

Image with description On a coordinate plane, the x axis lists negative 1 to 5 by 1 unit. The y axis lists negative 2 to 8 by 1 unit. The parabola opens up, has vertex at the origin, and passes through (negative 1 comma 2) and (1 comma 2). The curve goes through (0 comma 1), (1 comma 2), (2 comma 4), and (3 comma 8).

D

Image with description On a coordinate plane, the x axis lists negative 1 to 5 by 1, and the y axis lists negative 2 to 8 by 1. The graph has two smooth curves. The first smooth curve originates below the negative direction of the x axis, goes through (0 comma 0), and moves further up. The second smooth curve is a parabola that opens up and has a vertex at the origin. It goes through (1 comma 3) and moves up. Both curves touch each other at the origin.

15

Which statement is true?

A

The growth rate of the exponential function exceeds the growth rate of the linear function for 0 is less than or equal to x comma x is less than or equal to 3 .

B

The growth rate of the exponential function exceeds the growth rate of the linear function for 1 is less than or equal to x comma x is less than or equal to 3 .

C

The growth rate of the exponential function exceeds the growth rate of the linear function for negative 1 is less than or equal to x comma x is less than or equal to 1 .

D

The growth rate of the exponential function exceeds the growth rate of the linear function for negative 1 is less than or equal to x comma x is less than or equal to 3 .

16

For which pair of functions is the exponential consistently growing at a faster rate than the quadratic over the interval 0 is less than or equal to x comma x is less than or equal to 5 ?

A

Image with description On a coordinate plane, the x axis lists negative 1 to 5 by 1 unit. The y axis lists negative 2 to 8 by 1 unit. The parabola opens up, has vertex at the origin, and passes through (negative 1 comma 4) and (1 comma 4). The curve goes through (0 comma 1), (1 comma 2), (2 comma 4), and (3 comma 8).

B

Image with description On a coordinate plane, the x axis ranges from negative 1 to 5 with an interval of 1 unit. The y axis ranges from negative 2 to 8 with in interval of 1 unit. The parabola opens up, has vertex at the origin, and passes through (negative 1 comma 3) and (1 comma 3). The curve goes through the origin, (1 comma 1), (2 comma 3), and (3 comma 7).

C

Image with description On a coordinate plane, the x axis lists negative 1 to 5 by 1 unit. The y axis lists negative 2 to 8 by 1 unit. The parabola opens up, has vertex at the origin, and passes through (negative 1 comma 2) and (1 comma 2). The curve goes through (0 comma 1), (1 comma 2), (2 comma 4), and (3 comma 8).

D

Image with description On a coordinate plane, the x axis lists negative 1 to 5 by 1 unit. The y axis lists negative 2 to 8 by 1 unit. The parabola opens up, has vertex at the origin, and passes through (2 comma 2) and (4 comma 8). The curve goes through (0 comma 1) and (1 comma 4).

17

Over which interval does the growth rate of the exponential function continue to exceed the growth rate of the linear function?

A

x is equal to 0 to x is equal to 3

B

x is equal to 0 point 3 8 to x is equal to 1 point 7 9

C

x is equal to 1 point 7 9 to x is equal to 3

D

x is equal to 0 to x is equal to 1 point 7 9

18

Which statement best describes the growth rates of the functions?

A

The exponential function grows faster than the quadratic function over only one interval; 2 is less than x comma x is less than or equal to 3 .

B

The exponential function grows faster than the quadratic function over the entire interval; 0 is less than x comma x is less than or equal to 4 .

C

The exponential function grows faster than the quadratic function over two intervals; 2 is less than x comma x is less than or equal to 4 .

D

The quadratic function grows faster than the exponential function over the entire interval; 0 is less than x comma x is less than or equal to 4 .

19

For which pair of functions is the exponential consistently growing at a faster rate than the quadratic over the interval 0 is less than or equal to x comma x is less than or equal to 5 ?

A

Image with description On a coordinate plane, the x axis lists negative 1 to 5 by 1 unit. The y axis lists negative 2 to 8 by 1 unit. The parabola opens up, has vertex at the origin, and passes through (negative 1 comma 4) and (1 comma 4). The curve goes through (0 comma 1), (1 comma 2), (2 comma 4), and (3 comma 8).

B

Image with description On a coordinate plane, the x axis lists negative 1 to 5 by 1 unit. The y axis lists negative 2 to 8 by 1 unit. The parabola opens up, has vertex at the origin, and passes through (negative 1 comma 2) and (1 comma 2). The curve goes through (0 comma 1), (1 comma 2), (2 comma 4), and (3 comma 8).

C

Image with description On a coordinate plane, the x axis lists negative 1 to 5 by 1, and the y axis lists negative 2 to 8 by 1. The graph has two smooth curves. The first smooth curve originates from the negative direction of the x axis, intersects the y axis at (0 comma 1), goes through (1 comma 4), and moves up. The second smooth curve is a parabola that opens up and has a vertex at the origin. It goes through (2, 2) and moves up.

D

Image with description On a coordinate plane, the x axis lists negative 1 to 5 by 1, and the y axis lists negative 2 to 8 by 1. The graph has two smooth curves. The first smooth curve originates below the negative direction of the x axis, goes through (0 comma 0), and moves further up. The second smooth curve is a parabola that opens up and has a vertex at the origin. It goes through (1 comma 3) and moves up. Both curves touch each other at the origin.

20

Over which interval does the growth rate of the exponential function exceed the growth rate of the linear function?

A

x is greater than 2

B

1 is less than or equal to x comma x is less than or equal to 2

C

0 is less than or equal to x comma x is less than or equal to 1

D

x is less than 1

Comparing Exponential, Linear, and Quadratic Growth — Quiz Answers

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