2020 AP Calculus Midterm Part 2

 $f\left(x\right)=\frac{x^2-x-42}{x^3+11x^2+30x}$  

A function f is defined by the given function, mark all of the following true statements

• one removable discontinuity

• two removable discontinuities

• three removable discontinuities

• two vertical asymptotes

• three vertical asymptotes

If g(x) is a continuous function for all values of a and b, then which of the following statements are true

• a = 0 and b = 0

• a = 1 and b = 2

• a = 4 and b = 8

• any real numbers where a = 2b

• any real numbers where 2a = b

f(x) is continuous on [-2,0] and some of the values of f are shown in the table. If f(x) =2 has no solution, then b could be

• -2

• 0

• 2

• 3

• none of these

A function f is continuous on [-2,2] and some of the values of f are shown in the given table. If f has only one root r on the closed interval [-2,2] and r is NOT 0, then a possible value of b is :

• -2

• -1

• 0

• 1

 $f\left(x\right)=\frac{x^2-x-42}{x^3+11x^2+30x}$  

Which of the following is the right end behavior model for f(x)?

• $\infty$

• $-\infty$

• 0

• $\frac{1}{x}$

• x

Which of the following represents the calculus method of determining a vertical asymptote?

Assume a is a real number

Mark all that apply

• 
• 
• 
• 

Which of the following represents the calculus method of determining a horizontal asymptote?

Assume a is a real number

Mark all that apply

• 
• 
• 
• 

Use the expression below to mark the correct statements
 $\frac{f\left(x+h\right)-f\left(x\right)}{h}$ 

• this is the AROC of f(x) from x to x +h

• this is the IROC of f(x) at x 

• this is the slope of the related secant line 

• this is the slope of the related tangent line 
  

Use the expression below to mark the correct statements
 $\lim_{h\rightarrow0}\frac{f\left(x+h\right)-f\left(x\right)}{h}$ 

• this is the AROC of f(x) from x to x +h

• this is the IROC of f(x) at x

• this is the slope of the related secant line

• this is the slope of the related tangent line