$\"\"$

\

The function is $\"\"$ .

\

The parent function is $\"\"$ .

\

Properties of power functions :

\

The graph of $\"\"$ is always contains the points $\"\"$ , $\"\"$ and $\"\"$ .

\

Graph the parent function $\"\"$ .

\

1). Draw a coordinate plane.

\

2). Plot the points and

\

3). Connect the points with smooth curve.

\

$\"\"$

\

$\"\"$

\

Consider the function $\"\"$ .

\

Vertical stretch:

\

The graph of $\"\"$ , stretches the graph of $\"\"$ vertically by a factor of $\"\"$ .

\

The graph of $\"\"$ contains the points $\"\"$ , $\"\"$ and $\"\"$ .

\

Horizontal shift:

\

The graph of $\"\"$ , shifts the graph of $\"\"$ horizontally at a distance of $\"\"$ units towards right.

\

\

The graph of $\"\"$ contains the points $\"\"$ , $\"\"$ and $\"\"$ .

\

Graph :

\

Draw the coordinate plane.

\

Plot the points.

\

Graph the transformed function $\"\"$ .

\

$\"\"$

\

$\"\"$

\

The function is $\"\"$ .

\

Vertical shift:

\

The graph of $\"\"$ shifts the graph of $\"\"$ a distance of $\"\"$ unit upward.

\

\

The graph of $\"\"$ contains the points $\"\"$ , $\"\"$ and $\"\"$ .

\

Graph :

\

Draw the coordinate plane.

\

Plot the points.

\

Graph the transformed function $\"\"$ .

\

$\"\"$

\

$\"\"$

\

The graph of $\"\"$ :

\

$\"\"$