Applying and analysing functions

When will a rational function have an oblique asymptote?

• When the degree of the numerator is less than the degree of the denominator.

• When the degree of the numerator is equal to the degree of the denominator.

• When the degree of the numerator is one greater than the degree of the denominator.

• When the degree of the numerator is greater than the degree of the denominator.

 $\frac{\left(x\ +\ 1\right)\left(x-4\right)}{\left(x-4\right)\left(x+7\right)}$  
State the values of x that must be excluded to prevent division by zero.

• -1, 4, and -7

• -1 and 4

• -4 and 7

• 4 and -7

 $f\left(x\right)=\frac{x+2}{x-5}$ 

What type of discontinuity is at x = 5 ?

• nonremovable discontinuity

• removable discontinuity

• jump discontinuity

• no discontinuity exists at x = 5

If the degree of the numerator < the degree of the denominator, what's the horizontal asymptote?

• y=0

• none

• fraction made by coefficients

What has to be true for a function to have a horizontal asymptote of y=0

• It has to be top heavy

• It has to be bottom heavy

• It has to be balanced

• It has to have a slant asymptote

• There is no horizontal asymptote

• y=4

• y=-3

• y=3

Which function has a horizontal asymptote $y=0$   ?

• 
• 
• 

What is the vertical asymptote of the following function?

• x = 2

• x = -2

• y = -3

• y = 3

Which of the following statements is true about the function below? $f\left(x\right)\ =\ \frac{x^3-9x}{3x^2-6x-9}$  

• There are two vertical asymptotes: x = 3 and x = -1

• There is one vertical asymptote at x = -1 and a hole at x = 3

• There are two holes: x = -3 and x = -1

• There are two vertical asymptotes: x = -3 and x = 1