EXAMPLE 1 Graph a square root function 1

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EXAMPLE 1 Graph a square root function 1 x , and state the domain

EXAMPLE 1 Graph a square root function 1 x , and state the domain and range. 2 Compare the graph with the graph of y = x. Graph y = SOLUTION Make a table of values and sketch the graph.

EXAMPLE 1 Graph a square root function The radicand of a square root must

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 = 1 x is a vertical shrink of the graph 2 1 of y = x by a factor of. 2

EXAMPLE 2 Graph a cube root function Graph y = – 3 3 x

EXAMPLE 2 Graph a cube root function Graph y = – 3 3 x , and state the domain and range. 3 Compare the graph with the graph of y = x. SOLUTION Make a table of values and sketch the graph.

EXAMPLE 2 Graph a cube root function The domain and range are all real

EXAMPLE 2 Graph a cube root function The domain and range are all real numbers. The graph of y = – 3 3 x is a vertical stretch of the 3 graph of y = x by a factor of 3 followed by a reflection in the x-axis.

EXAMPLE 3 Solve a multi-step problem Pendulums The period of a pendulum is the

EXAMPLE 3 Solve a multi-step problem 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 l where l is the pendulum’s length (in feet). • Use a graphing calculator to graph the model. • How long is a pendulum with a period of 3 seconds?

EXAMPLE 3 Solve a multi-step problem SOLUTION STEP 1 Graph the model. Enter the

EXAMPLE 3 Solve a multi-step problem SOLUTION STEP 1 Graph the model. Enter the equation y = 1. 11 x. The graph is shown below. STEP 2 Use the trace feature to find the value of x when y = 3. The graph shows x 7. 3.

EXAMPLE 3 Solve a multi-step problem ANSWER A pendulum with a period of 3

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

GUIDED PRACTICE for Examples 1, 2 and 3 1. y = – 3 x SOLUTION Make a table of values and sketch the graph. ANSWER Domain: x > 0 Range: y < 0

GUIDED PRACTICE 2. y = for Examples 1, 2 and 3 1 x 4

GUIDED PRACTICE 2. y = for Examples 1, 2 and 3 1 x 4 SOLUTION Make a table of values and sketch the graph. x 1 y 0. 25 2 3 0. 35 0. 43 4 0. 5 ANSWER Domain: x > 0 Range: y < 0

for Examples 1, 2 and 3 GUIDED PRACTICE 3. y = – 1 3

for Examples 1, 2 and 3 GUIDED PRACTICE 3. y = – 1 3 x 2 SOLUTION Make a table of values and sketch the graph. x y -3 -2 0. 72 0. 63 -1 0 0. 5 0 1 2 3 -0. 5 -0. 6 -0. 7 ANSWER Domain: All real numbers Range: All real numbers

for Examples 1, 2 and 3 GUIDED PRACTICE 3 4. g(x) = 4 x

for Examples 1, 2 and 3 GUIDED PRACTICE 3 4. g(x) = 4 x SOLUTION Make a table of values and sketch the graph. x y -3 -2 -5. 77 -5. 04 -1 0 1 -4 0 4 2 3 5. 04 5. 77 ANSWER Domain: All real numbers Range: All real numbers

GUIDED PRACTICE for Examples 1, 2 and 3 5. What if ? Use the

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