Unit 1 Review

• 0

• -1

• 1

• nonexistent

Let f(x) be the piecewise function defined above. For what value of k is f(x) continuous at x = -2?

• -1

• 0

• 1

• 2

• II only

• III only

• I and II only

• I, II, and III

Let f be a function that is continuous on the closed interval [1,3] with f(1) = 4 and f(3) = 10. Which of the following is guaranteed to be true?

• f(2) = 7

• f(x) = 2 for some x on the interval (1, 3)

• f(x) = 8 for some x on the interval (1, 3)

• None of the above

For which of the following does the limit of f(x) exist as x approaches 4?

• I only

• III only

• I and II only

• I and III only

If f(x) is a rational function and has a vertical asymptote at x = 1, which of the following statements must be false?

• 
• 
• 
• 

• -4

• -1

• 1

• 4

The graph of f is shown. What is the limit as x approaches zero of f(x)*f(-x)?

• 4

• -4

• 2

• -2

• The limit does not exist

Let y = a be the horizontal asymptote of f. Let x = b the vertical asymptote of f. What is a - b?

• -1

• 7

• 1

• -7

Determine whether the function f(x) is continuous or discontinuous at x = 2 and why.

• The function is continuous because the limit of f as x approaches 2 from the left equals the limit of f as x approaches 2 from the right.

• The function is NOT continuous because the limit of f as x approaches 2 from the left DOES NOT equal the limit of f as x approaches 2 from the right.

• The function is NOT continuous because the limit of f as x approaches 2 from the left equals the limit of f as x approaches 2 from the right BUT does not equal f(2).

• The function is NOT continuous because f has a removable discontinuity at x = 2.