Quiz about Graphing Rational Functions

Question 1

How could you obtain the graph of $$g\left(x\right)=\frac{2}{x-5}-3$$ from the graph of f(x) = $$\frac{2}{x}$$ ?

Accepted Answer

Shift the graph of f(x) 5 units to the right and 3 units down.

Answer

Shift the graph of f(x) 5 units to the left and 3 units up.

Answer

Shift the graph of f(x) 5 units to the left and 3 units down.

Answer

Shift the graph of f(x) 5 units to the right and 3 units up.

Question 2

How do the graphs of $$f\left(x\right)=\frac{1}{x+2}and\ g\left(x\right)=\frac{3}{x+2}$$

Accepted Answer

The function f(x) is vertically stretched to obtain the graph of g(x).

Answer

The function f(x) is horizontally stretched to obtain the graph of g(x).

Answer

The function f(x) is shifted vertically to obtain the graph of g(x).

Answer

The function f(x) is shifted horizontally to obtain the graph of g(x).

Question 3

Question 3.

Accepted Answer

$$h\left(x\right)=\frac{x^3-4x}{x}$$

Answer

$$f\left(x\right)=x^2-4x$$

Answer

$$g\left(x\right)=x^2-4$$

Answer

$$j\left(x\right)=\frac{x^2-4}{x}$$

Question 4

What are the asymptotes of f(x)= $$\frac{8}{x^2}$$

Accepted Answer

The vertical asymptote is the line x = 0. The horizontal asymptote is the line y = 0.

Answer

The function f(x) has no asymptotes.

Answer

The vertical asymptote is the line x = 8. The horizontal asymptote is the line y = 8.

Answer

The vertical asymptote is the line y = 0. The horizontal asymptote is the line x = 0.

Question 5

Which function(s) have a removable discontinuity? Select all that apply.

Accepted Answer

$$g\left(x\right)=\frac{x^2-3x-4}{x+1}$$

Accepted Answer

$$j\left(x\right)=\frac{x^2-4}{x+2}$$

Answer

$$f\left(x\right)=\frac{x+1}{x-1}$$

Answer

$$h\left(x\right)=\frac{x^2-3x-4}{x+4}$$

Question 6

In which quadrants does the graph of y = $$\frac{1}{x^3}$$ exist? Select all that apply.

Accepted Answer

<p>Quadrant I</p>

Accepted Answer

Quadrant III

Answer

Quadrant II

Answer

Quadrant IV

Question 7

Which statement about an extraneous solution is not correct? Select all that apply

Accepted Answer

It comes from correct solution steps and is a valid solution of the equation.

Accepted Answer

. It comes from incorrect solution steps and is a valid solution of the equation.

Accepted Answer

It comes from incorrect solution steps and is not a valid solution of the equation.

Answer

It comes from correct solution steps and is not a valid solution of the equation.

Graphing Rational Functions