Chapter 6.5, Problem 3CFU

a.

To determine

To find: the variable that could be changed to stretch the graph vertically.

Answer to Problem 3CFU

  $A$

Explanation of Solution

Given information:

  $y=A\sin \left(k\theta -c\right)+h$

Calculation:

In order to stretch the graph vertically, the whole function should be multiplied by A . Thus the variable $A$ should be increased.

b.

To determine

To find: the variable that could be changed to translate the graph downward vertically.

Answer to Problem 3CFU

  $h$

Explanation of Solution

Given information:

  $y=A\sin \left(k\theta -c\right)+h$

Calculation:

In order to translate the graph vertically downward, the whole function should be subtracted by $h$ . Thus the variable $h$ should be decreased.

c.

To determine

To find: the variable that could be changed to shrink the graph horizontally.

Answer to Problem 3CFU

  $k$

Explanation of Solution

Given information:

  $y=A\sin \left(k\theta -c\right)+h$

Calculation:

In order to shrink the graph horizontally, multiply $\theta$ by $k<1$ . Thus the variable $k$ should be decreased.

d.

To determine

To find: the variable that could be changed to translate the graph to the right.

Answer to Problem 3CFU

  $c$

Explanation of Solution

Given information:

  $y=A\sin \left(k\theta -c\right)+h$

Calculation:

In order to translate the graph to the right, add $c<0$ to $k\theta$ . Thus the variable $c$ should be decreased.