$\"\"$

The trigonometric function is $\"\"$ .

The graph of $\"\"$ is the graph of $\"\"$ compressed vertically by $\"\"$ units and shrinks horizontally by $\"\"$ units.

Compare the function $\"\"$ with $\"\"$ .

$\"\"$ .

Amplitude is $\"\"$ .

Period $\"\"$ .

$\"\"$

Consider an interval $\"\"$ .

Solve the equations :

$\"\"$ and $\"\"$

The interval $\"\"$ corresponds to one cycle of the graph.

Divide this interval into four equal parts to produce the key points.

Construct the table of values in the interval $\"\"$ :

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

The above function has vertical asyptotes at $\"\"$ , $\"\"$ , and $\"\"$ , ........

$\"\"$

Graph :

1). Draw the co-ordinate plane.

2). Plot the key points.

3). Draw the vertical asyptotes at $\"\"$ , $\"\"$ , and $\"\"$ .

4). Sketch the graph, connected through those key points with a smooth curve.

$\"\"$

The graph of $\"\"$ is :

$\"\"$