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has an intercept at (0, 0). The graph is symmetric

with respect to the y-axis. The graph is continuous.

and

. The graph is

1-5 Parent Functions and Transformations

decreasing on (− , 0) and increasing on (0,

).

Describe the following characteristics of the

5.

f (x) = c

graph of each parent function: domain, range,

ANSWER:

intercepts, symmetry, continuity, end behavior,

and intervals on which the graph is

D = {x | x

R}, R = {y | y = c, c

R}. If c = 0, all

increasing/decreasing.

real numbers are x-intercepts. If c ≠ 0, there are no

1.

f (x) = §x¨

x-intercepts. The graph has a y-intercept at (0, c). If

c ≠ 0, the graph is symmetric with respect to the y-

ANSWER:

axis. If c = 0, the graph is symmetric with respect to

D = {x | x

R}, R = {y | y

Z}. The graph has a y-

the x-axis, y-axis, and origin. The graph is

intercept at (0, 0) and x-intercepts for {x | 0 ≤ x < 1,

continuous.

and

. The

x

R}. The graph has no symmetry. The graph has

graph is constant on (− , ).

a jump discontinuity for {x | x

Z}.

= −

6.

=

and

. The graph is constant for {x | x

f (x) = x

Z}. The graph increases for {x | x

Z}.

ANSWER:

D = {x | x

R}, R = {y | y R}. The graph has an

intercept at (0, 0). The graph is symmetric with

2.

f (x) =

respect to the origin. The graph is continuous.

and

. The graph is

ANSWER:

increasing on (− , ).

D = {x | x ≠ 0, x

R}, R = {y | y ≠ 0, y

R}. The

graph has no intercepts. The graph is symmetric with

Use the graph of f (x) =

to graph each

respect to the origin. The graph has an infinite

function.

discontinuity at x = 0.

= 0 and

=

7.

g(x) =

0. The graph is decreasing on (− , 0) and (0,

).

ANSWER:

3

3.

f (x) = x

ANSWER:

D = {x | x

R}, R = {y | y

R}. The graph has an

intercept at (0, 0). The graph is symmetric with

respect to the origin. The graph is continuous.

= −

and

=

. The graph is

increasing on (− , ).

4

4.

f (x) = x

8.

g(x) =

ANSWER:

ANSWER:

D = {x | x

R}, R = {y | y ≥ 0, y

R}. The graph

has an intercept at (0, 0). The graph is symmetric

with respect to the y-axis. The graph is continuous.

and

. The graph is

decreasing on (− , 0) and increasing on (0,

).

5.

f (x) = c

ANSWER:

D = {x | x

R}, R = {y | y = c, c

R}. If c = 0, all

9.

g(x) =

– 4

real numbers are x-intercepts. If c ≠ 0, there are no

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Page 1

x-intercepts. The graph has a y-intercept at (0, c). If

ANSWER:

c ≠ 0, the graph is symmetric with respect to the y-

axis. If c = 0, the graph is symmetric with respect to

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