Graphing rational functions Quiz 1

Question 1

The x- and y-intercept of $$f\left( x \right) = \dfrac{{2x + 4}}{{4 - x}}$$ are

Accepted Answer

$$\left( { - 2,0} \right)$$ and $$\left( {0,1} \right)$$

Answer

$$\left( {1,0} \right)$$; no y-intercept

Answer

$$\left( {1,0} \right)$$ and $$\left( {0, - 2} \right)$$

Answer

no x-intercept; $$\left( {0,1} \right)$$

Question 2

The function $$f\left( x \right) = \dfrac{{{x^2} - 3}}{{{x^2} + 4}}$$ is positive in the range.

Accepted Answer

$$\left( { - \sqrt 3 ,\sqrt 3 } \right)$$

Answer

$$\left( { - \infty , - \sqrt 3 } \right) \cup \left( {\infty ,\sqrt 3 } \right)$$

Answer

$$\left( { - \infty ,\infty } \right)$$

Answer

$$\left( { - \dfrac{{\sqrt 3 }}{2},\dfrac{{\sqrt 3 }}{2}} \right)$$

Question 3

The number of vertical asymptotes for  $$f\left( x \right) = \dfrac{{{x^2} + 4}}{{4 - {x^2}}}$$

Accepted Answer

$$2$$

Answer

$$0$$

Answer

$$3$$

Answer

$$1$$

Question 4

If the horizontal asymptote of the function $$f\left( x \right) = \dfrac{{kx}}{{x - 3}}$$ is $$y = 4$$, then the value of $$k$$ is

Accepted Answer

$$4$$

Answer

$$12$$

Answer

$$2$$

Answer

$$3$$

Question 5

The asymptotes of the function $$f\left( x \right) = \dfrac{{{x^2} + 25}}{{{x^2} - 9}}$$ intersects at

Accepted Answer

$$\left( { - 3,1} \right)$$ and $$\left( {3,1} \right)$$

Answer

$$\left( {3,1} \right)$$

Answer

$$\left( { - 1,1} \right)$$ and $$\left( {1,1} \right)$$

Answer

$$\left( {1, - 3} \right)$$ and $$\left( {1,3} \right)$$