The period $\"\"$ (in seconds) of a simple pendulum is a function of its $\"\"$ (in feet).

The equation is $\"\"$ , where $\"\"$ feet per second per second is the acceleration of gravity.

(a) Graph the function $\"\"$ .

Write the function $\"\"$ in terms of $\"\"$ .

Substitute $\"\"$ in $\"\"$ .

$\"\"$

Graph the function $\"\"$ :

$\"\"$

(b) Graph the functions $\"\"$ , $\"\"$ , and $\"\"$ .

$\"\"$ , shift the graph of $\"\"$ $\"\"$ units to the left.

$\"\"$

The graph of $\"\"$ is obtained from $\"\"$ by shifting $\"\"$ unit to the left.

The graph of $\"\"$ is obtained from $\"\"$ by shifting $\"\"$ units to the left.

Graph:

$\"\"$

(c)

Observe the graph in part (b), adding to the length $\"\"$ changes the period $\"\"$ is increasing.

By lengthening the pendulum, more time is required for it to complete a given period.

(d) Graph the functions $\"\"$ , $\"\"$ , and $\"\"$ .

Compress the graph of $\"\"$ horizontally.

The graph of $\"\"$ is obtained from $\"\"$ by compress the graph of $\"\"$ horizontally factor of $\"\"$ .

$\"\"$

(e) Observe the graph in part (b),

Multiplying the length $\"\"$ by factors of $\"\"$ , $\"\"$ , and $\"\"$ changes the period. $\"\"$ is increasing.

By multiplying the length $\"\"$ by factors of $\"\"$ , $\"\"$ and $\"\"$ of the pendulum, more and more time is required for it to complete a given period.

(a)

Graph of the function $\"\"$ :

$\"\"$

(b) Graph of the functions $\"\"$ , $\"\"$ , and $\"\"$ .

$\"\"$

(c)

adding to the length $\"\"$ changes the period $\"\"$ is increasing.

By lengthening the pendulum, more time is required for it to complete a given period.

(d) Graph of the functions $\"\"$ , $\"\"$ , and $\"\"$ .

$\"\"$

(e)

Multiplying the length $\"\"$ by factors of $\"\"$ , $\"\"$ , and $\"\"$ changes the period. $\"\"$ is increasing.

By multiplying the length $\"\"$ by factors of $\"\"$ , $\"\"$ and $\"\"$ of the pendulum, more and more time is required for it to complete a given period.