Chapter 8.3, Problem 55PPSE

Solution

To Graph: The equation $y=\frac{3}{x}+4$ and sketch the asymptotes. Also identify the domain and range.

Given information:

The given function is $y=\frac{3}{x}+4$ .

Explanation:

Consider the given function.

The function $y=\frac{a}{x-h}+k$ has a vertical asymptote at $x=h$ and a horizontal asymptote of $y=k$ , where a determines whether the graph of $y=\frac{1}{x}$ stretches, shrinks or reflects.

Observe the graph of $y=\frac{3}{x}+4$ , the graph of $y=\frac{1}{x}$ is shifted 4 units up.

Therefore, its horizontal asymptote is at $x=0$ and its vertical asymptote is at $y=4$ with domain of all real numbers except 0 and range of all real number except 4.

The required graph is shown below:

  

Interpretation: The domain is all real numbers except 0 and range is all real number except 4.