Question

Graph the function. Be sure to label all the intercepts. [Hint: Notice that the function is half an ellipse.]

Answer 1

Step 1:

The function .

Change to .

The function is half an ellipse.

Convert the above equation in standard form of ellipse.

Square on both sides.

Compare it to standard form of vertical ellipse (Center at origin)

Where .

is length of semi major axis and is semi minor axis.

In this case , center at .

Major axis length is 8 units and minor axis length is 4 units.

Step 2:

Graph:

Draw the coordinate plane.

Plot the center at .

The function is square root function. So negative  values is not possible.

Draw the minor axis and positive part of major axis.

Sketch the top part of ellipse in first and second quadrants only.

Observe the graph: The -intercepts are and  -intercept is .

Solution:

The -intercepts are and  -intercept is .