Question Type 2: Graphing functions for different pairs of a,b,c in (x+a)/(x+b)(x+c) to test different looks of graphs Exercises

Consider the function $f(x) = \frac{x+1}{(x-1)(x+1)}$.

Determine the domain, any holes, asymptotes, intercepts, and end behavior. Hence, sketch the graph of $f$.

For $f(x)=\frac{x}{(x+2)(x+3)}$, determine its domain, asymptotes, intercepts, end behavior, and sketch via technology.

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

Find the domain, holes, asymptotes, intercepts, and end behavior of the function. Sketch the graph of $f$ using technology.

Analyze and graph $f(x)=\frac{x-2}{(x+1)(x+4)}$: find domain, asymptotes, intercepts, end behavior, and sketch using technology.

For the function $f(x)=\frac{x+6}{(x+2)(x+3)}$, determine its domain, vertical and horizontal asymptotes, intercepts, end behavior, and sketch its graph using technology.

Sketch the graph of $f(x) = \frac{x-5}{(x-3)(x+1)}$. Clearly state the equations of any asymptotes, the coordinates of any axes intercepts, and the domain.

Sketch $f(x)=\frac{x+1}{(x+2)(x+3)}$ by finding its domain, asymptotes, intercepts, end behavior, and using technology for the graph.

Analyze and graph $f(x)=\frac{x+6}{(x-2)(x+4)}$: find the domain, asymptotes, intercepts, end behavior, and sketch the graph using technology.

Determine the graph of $f(x)=\frac{x-3}{(x+1)(x-2)}$: find domain, asymptotes, intercepts, end behavior, and sketch with technology.

Sketch $f(x)=\frac{x+4}{(x+2)(x-3)}$ after finding its domain, vertical and horizontal asymptotes, intercepts, end behavior, and graphing with technology.