Rational Functions Test Review

Consider the function given by $$f(x)=\frac{(x^2-4x-12)}{(x^2+6x+8)}$$ . The function f has a vertical asymptote at $$x=a$$ and a horizontal asymptote at $$y=b$$ . What is the value of $$a+b$$ ?

Which of the following is a graph of the function $$y=\frac{1}{x}$$ ?

The parent graph $$f(x)=\frac{1}{x}$$ has been changed by the transformation $$-2f(x+1)-2$$ . Choose TWO points that are located on the graph of the transformed function by selecting the appropriate circles.

The graph of $$f(x)=\frac{1}{x}$$ is transformed to create the graph of $$g(x)=\frac{1}{(x-3)}+7$$ . Choose the correct answer from each drop-down menu to complete the statement. To create g, the graph of f is translated ​ (a)   units to the ​ (b)   and ​ (c)   units ​ (d)   .

Find the solution to the equation. $$\frac{1}{(x-8)}-1=\frac{7}{(x-8)}$$ . Enter the correct number. (only the number)

What is the solution to the equation? $$\frac{3}{(x+2)}-\frac{2}{(x^2-4)}=\frac{1}{(x-2)}$$ . Enter your number. (only the number)

What is the domain and the vertical asymptote of the function $$f(x)=\frac{(3x-2)}{(x+5)}$$ ? Move the correct answer to each box.

Vertical Asymptote: ​ (a)  

Domain: (b)  

Consider the rational function below: $$f(x)=\frac{2x^2-10x+12}{(x^2-4)(x+3)}$$ . Determine which of the following equations represent a vertical asymptote of the graph of f. Choose the correct answer in each row.

Consider the rational function below: $$f(x)=\frac{1}{x-5}+2$$ .

The Vertical asymptote of f is ​ (a)   and the domain of f is ​ (b)  

Consider the rational expressions $$\frac{5}{x+4}$$ and $$\frac{x+4}{x-4}$$ that are defined for all x in their domains. What are the sum and product of these two expressions? Move the correct answer to each box.

Sum: ​ (a)  

Product: ​ (b)