EXAMPLE 1 Graph a square root function

Graph y = ,and state the domain and range.

Compare the graph with the graph of y = .

12

x

x

SOLUTION

Make a table of values and sketch the graph.

EXAMPLE 1 Graph a square root function

The radicand of a square root must be nonnegative.

So, the domain is x ≥ 0. The range is y ≥ 0.

The graph of y = is a vertical shrink of the graph

of y = by a factor of .

x12

x 12

EXAMPLE 2 Graph a cube root function

Graph y = –3 3 , and state the domain and range. Compare the graph with the graph of y = .

xx3

SOLUTION

Make a table of values and sketch the graph.

EXAMPLE 2 Graph a cube root function

The domain and range are all real numbers.

The graph of y = – 3 is a vertical stretch of the

graph of y = by a factor of 3 followed by a

reflection in the x-axis.

x3

x3

EXAMPLE 3 Solve a multi-step problem

• Use a graphing calculator tograph the model.

• How long is a pendulumwith a period of 3 seconds?

Pendulums

The period of a pendulum is the time the pendulum takes to complete one back-and-forth swing. The period T (in seconds) can be modeled by T = 1.11 where l is the pendulum’s length (in feet).

l

EXAMPLE 3 Solve a multi-step problem

SOLUTION

STEP 1Graph the model. Enter the equation y = 1.11 . The graph is shown below.

xUse the trace feature to find the value of x when y = 3.The graph shows x 7.3.

STEP 2

EXAMPLE 3 Solve a multi-step problem

ANSWER

A pendulum with a period of 3 seconds is about 7.3 feet long.

GUIDED PRACTICE for Examples 1, 2 and 3

1. y = – 3 x

SOLUTION

ANSWER

Domain: Range:x > 0 y < 0

Make a table of values and sketch the graph.

GUIDED PRACTICE for Examples 1, 2 and 3

SOLUTION

ANSWER

Domain: Range:x > 0 y < 0

2. y =14

x

Make a table of values and sketch the graph.

x 1 2 3 4

y 0.25 0.35 0.43 0.5

GUIDED PRACTICE for Examples 1, 2 and 3

3. y = x312

–

ANSWER

Domain: Range:All real numbers All real numbers

x -3 -2 -1 0 1 2 3

y 0.72 0.63 0.5 0 -0.5 -0.6 -0.7

SOLUTION

Make a table of values and sketch the graph.

GUIDED PRACTICE for Examples 1, 2 and 3

4. g(x) = 4 x3

ANSWER

Domain: Range:All real numbers All real numbers

x -3 -2 -1 0 1 2 3

y -5.77 -5.04 -4 0 4 5.04 5.77

SOLUTION

Make a table of values and sketch the graph.

GUIDED PRACTICE for Examples 1, 2 and 3

5. What if ? Use the model in example 3 to find the length of a pendulum with a period of 1 second. ANSWER

About 0.8 ft