Question Type 3: Graphing different rational functions, including the intercepts and the asymptotes Exercises

Sketch the graph of the function $f(x)=\frac{5x+8}{7x+9}$. Find its domain, x-intercept, y-intercept, vertical asymptote, and horizontal asymptote.

Consider the function $f(x)=\frac{x^2+4x+3}{x+1}$.

Find the domain, intercepts, and any holes or asymptotes. Hence, sketch the graph of $f$.

Sketch the graph of the function $f(x)=\frac{4x^2+2x-3}{2x-1}$. Find its intercepts, vertical asymptote, and oblique asymptote.

For $f(x)=\frac{x^2-4}{x-2}$, find any holes, intercepts, and asymptotes, then sketch the graph.

For the function $f(x)=\frac{2x^2-3x+1}{x-1}$, determine the intercepts and the equations of the vertical and oblique asymptotes. Sketch the graph of $f(x)$.

For $f(x)=\frac{3x^2-5x+2}{x-2}$, determine intercepts, asymptotes (vertical and oblique), and sketch the graph.

Sketch

Determine all intercepts, vertical asymptotes, horizontal asymptote, and any holes.

Sketch the graph of $f(x)=\frac{2x+3}{x-1}$. State the coordinates of the axes intercepts and the equations of all asymptotes.

Sketch $f(x)=\frac{x^2+x-6}{x+3}$. Identify the domain, holes or asymptotes, and intercepts.

Sketch the graph of $f(x)=\frac{5}{x+2}$. State its intercepts and asymptotes.

Find the domain, intercepts, and asymptotes of the function $f(x)=\frac{3x-1}{2x+5}$. Sketch the graph of $f$.

Sketch the graph of $f(x)=\frac{x^3-1}{x^2-1}$. Identify the domain, holes, vertical asymptotes, oblique asymptote, and axes intercepts.