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Chapter 11: Q9. (page 699)

Identify the asymptotes of the function.

y=2x鈭�4

Short Answer

Expert verified

The vertical asymptote:x=4

The horizontal asymptote:y=0

Step by step solution

01

Step 1. Define a rational function.

A function of the form y=pqis called a rational function, where p andq are the polynomials and q鈮�0.

02

Step 2. Define the asymptotes for the rational function in the form y=ax−b+c.

A rational function in the form y=ax鈭�b+c,鈥夆赌�a鈮�0, has a vertical asymptote at the x-value that makes the denominator equal zero,x=b and it has a horizontal asymptote at y=c.

03

Step 3. Calculate the asymptotes for the function y=2x−4.

Observe the rational function y=2x鈭�4.

For vertical asymptote,

Denominator=0

x鈭�4=0x=4

So,x=鈭�2 is the vertical asymptote.

For horizontal asymptote,

y=c

Since, c=0.

So, y=0is the horizontal asymptote.

Therefore,

The vertical asymptote: x=4

The horizontal asymptote:y=0

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