Quiz about Algebra 2 Rational Function Quiz

Question 1

What is the Horizontal Asymptote (H.A.) for the given rational function?

$$f\left(x\right)=\frac{7}{2x-4}$$

Accepted Answer

H.A.: $$y=0$$

Answer

H.A.: $$y=2$$

Answer

H.A.: $$y=\frac{7}{2}$$

Answer

H.A.: $$x=2$$

Question 2

What is the Vertical Asymptote (V.A.) of the given rational function?

$$f\left(x\right)=\frac{2x+9}{4x-6}$$

Accepted Answer

V.A.: $$x=\frac{3}{2}$$

Answer

V.A.: $$x=\frac{1}{2}$$

Answer

V.A.: $$x=\frac{-9}{2}$$

Answer

V.A.: $$x=0$$

Question 3

Determine the Vertical Asymptote (V.A.) of the given rational function.

$$f\left(x\right)=\frac{5x+20}{4x}$$

Accepted Answer

$$x=0$$

Answer

$$y=\frac{5}{4}$$

Answer

$$x=-4$$

Answer

$$x=1$$

Question 4

Determine the Horizontal Asymptote (H.A.) of the given rational function.

$$f\left(x\right)=\frac{-3x+9}{6x-5}$$

Accepted Answer

$$y=\frac{-1}{2}$$

Answer

$$y=3$$

Answer

$$y=\frac{5}{6}$$

Answer

$$x=0$$

Question 5

What is the x-intercept of the given rational function?

$$f\left(x\right)=\frac{4x-12}{2x+7}$$

Accepted Answer

$$\left(3,\ 0\right)$$

Answer

$$\left(0,\ 2\right)$$

Answer

$$\left(2,\ 0\right)$$

Answer

$$\left(\frac{-7}{2},\ 0\right)$$

Question 6

What is the y-intercept of the given rational function?

$$f\left(x\right)=\frac{4x+16}{3x+4}$$

Accepted Answer

(0, 4)

Answer

(-4, 0)

Answer

$$\left(\frac{-4}{3},\ 0\right)$$

Answer

$$\left(\frac{4}{3},\ 0\right)$$

Question 7

What is the Slant Asymptote (S.A.) for the given rational function? [Hint: use long division method]

$$f\left(x\right)=\frac{8x^2+16x-3}{2x+3}$$

Accepted Answer

$$y=4x+2$$

Answer

$$y=-3x-2$$

Answer

$$y=2x+3$$

Answer

$$y=-4x-2$$

Question 8

Which graph represents the given rational function?

$$f\left(x\right)=6-\frac{4}{x+2}$$

Accepted Answer

Question 9

Which graph represents the given rational function?

$$f\left(x\right)=\frac{-2x+9}{3x+5}$$

Accepted Answer

Question 10

Which graph represents the given rational function?

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

Accepted Answer

Question 11

What is the Slant Asymptote (S.A.) of the given rational function?

$$f\left(x\right)=\frac{3x^2+14x+2}{x+4}$$

Accepted Answer

$$y=3x+2$$

Answer

$$y=x-4$$

Answer

$$y=-3x+2$$

Answer

$$y=3x-2$$

Question 12

Determine the x-intercept of the given rational function.

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

Accepted Answer

$$\left(-\frac{5}{2},\ 0\right)$$

Answer

$$\left(0,\ 1.75\right)$$

Answer

$$\left(0,\ -2\right)$$

Answer

$$\left(-4,\ 0\right)$$

Question 13

Determine the y-intercept of the given rational function.

$$f\left(x\right)=\frac{3x-10}{2x+5}$$

Accepted Answer

$$\left(0,\ -2\right)$$

Answer

$$\left(\frac{10}{3},\ 0\right)$$

Answer

$$\left(0,\ \frac{3}{2}\right)$$

Answer

$$\left(-3,\ 0\right)$$

Question 14

Determine the Horizontal Asymptote (H.A.) of the given rational function.

$$f\left(x\right)=\frac{8x}{2x+3}+5$$

Accepted Answer

$$y=9$$

Answer

$$y=0$$

Answer

$$y=4$$

Answer

$$y=\frac{-3}{2}$$

Question 15

Determine the Horizontal Asymptote (H.A.) of the given rational function.

$$f\left(x\right)=\frac{10}{5x+9}+4$$

Accepted Answer

$$y=4$$

Answer

$$x=2$$

Answer

$$y=\frac{-9}{5}$$

Answer

$$y=0$$

Algebra 2 Rational Function Quiz

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