example 1 graph a square root function graph y =,and state the domain and range. compare the graph...
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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
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