PreCalculus Honors

Unit Test #3

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No Calculator Allowed

 

For all questions on this test, let f x = x 3 x 2 2x x 2 4 .

 

1.

The graph of f x has one hole. Give its coordinates.

(3)

First, the factorization: x x2 x+1 x+2 x2 . The common factor of x2 indicates a hole at x=2; its y-coordinate is at 2 2+1 2+2 = 3 2 . For all other questions, the rational function is really x x+1 x+2 = x 2 +x x+2 .

 

2.

The graph of f x has one vertical asymptote. Give its equation.

(3)

It is at x=2.

 

3.

The graph of f x has two axis intercepts. Give their coordinates.

(4)

They are at 0,0 and 1,0 .

 

4.

Determine the equation of the end behavior asymptote of f x .

(4)

Division time!

2 1 1 0 2 2 1 1 2

The end behavior asymptote is at y=x1.

 

5.

Give a labeled sketch of the graph of f x in the space below.

(10)

An Image

 


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