Chapter 11, Problem 6PT

To determine

Find the asymptotes of the function $y=\frac{1}{x}+3$ and then graph it.

Answer to Problem 6PT

Vertical asymptote: x = 0 and Horizontal Asymptote y = 3

Explanation of Solution

Given:

Find the asymptotes of the function $y=\frac{1}{x}+3$ and then graph it.

Concept Used:

To find the vertical asymptote(s) of a rational function, simply set the denominator equal to 0 and solve for x. We must set the denominator equal to 0 and solve.

The vertical asymptotes will occur at those values of x for which the denominator is equal to zero.

Horizontal Asymptotes CAN be crossed. To find horizontal asymptotes: If the degree (the largest exponent) of the denominator is bigger than the degree of the numerator, the horizontal asymptote is the x-axis (y = 0). If the degree of the numerator is bigger than the denominator, there is no horizontal asymptote

Calculation:

Vertical asymptote: x = 0 and Horizontal Asymptote y = 3

The graph of the function: $y=\frac{1}{x}+3$

  

Thus, Vertical asymptote: x = 0 and Horizontal Asymptote y = 3