Combine a translation and a reflection

1
EXAMPLE 4
Combine a translation and a reflection
SOLUTION
STEP 1
Identify the amplitude, period, horizontal shift,
and vertical shift.
STEP 2
Draw the midline of the graph. Because k 0,
the midline is the x-axis.
2
EXAMPLE 4
Combine a translation and a reflection
3
EXAMPLE 4
Combine a translation and a reflection
STEP 5
Draw the graph through the key points.
4
EXAMPLE 5
Combine a translation and a reflection
Graph y 3 tan x 5.
SOLUTION
STEP 1
Identify the period, horizontal shift, and
vertical shift.
STEP 2
Draw the midline of the graph, y 5.
STEP 3
5
EXAMPLE 5
Combine a translation and a reflection
STEP 4
Reflect the graph. Because a lt 0, the graph is
reflected in the midline y 5.
6
EXAMPLE 5
Combine a translation and a reflection
STEP 5
Draw the graph through the key points.
7
EXAMPLE 6
Model with a tangent function
8
EXAMPLE 6
Model with a tangent function
SOLUTION
Use a tangent function to write an equation
relating d and q .
Definition of tangent
Multiply each side by 120.
Subtract 260 from each side.
Solve for d.
The graph of d 120 tan q 260 is shown at
the right.
9
for Examples 4, 5, and 6
GUIDED PRACTICE
Graph the function.
4.
SOLUTION
10
for Examples 4, 5, and 6
GUIDED PRACTICE
Graph the function.
SOLUTION
11
for Examples 4, 5, and 6
GUIDED PRACTICE
Graph the function.
SOLUTION
12
for Examples 4, 5, and 6
GUIDED PRACTICE