Chapter 1: Functions from a Calculus Perspective

If j(x) = x² + 1, find j(a + 1).

• a² + 2a + 2

• a² + a + 1

• a² + a + 2

• a² + 2a + 1

State the domain of the function

 $f\left(x\right)=\frac{x^2+1}{x^2-3x}$ 

• all real numbers except 0, 1, and 3

• all real numbers except 0 and 3

• all real numbers except 0

• all real numbers except 3

The roots of the equation x² - 8x - 20 = 0 are ____.

• 2 and 10

• -2 and 10

• -2 and -10

• 2 and -10

Find the vertex (the turning point) of the graph of f(x) = x² + 4x - 5.

• (-2, -9)

• (-2, 9)

• (0, -5)

• (2, 7)

Consider the graph of f(x) shown. Which of the following corresponds to the function value at x = –3?

• 5

• -2

• -8

• 2

Use the graph of f to find the domain and range of the function.

• D = (−3, 3], R = [–3, 0]

• D = [−3, 3), R = [–3, 0]

• D = (−3, 3), R = [–3, 0]

• D = [−3, 3], R = [–3, 0]

Determine whether the function  $f\left(x\right)=\frac{x+1}{x^2-1}$  is continuous at x = 1. 

• Yes, it is continuous at x = 1, but not at x = -1.

• None is correct.

• No, because substituting x = 1 results in a denominator of 0.

• Yes, the inability to divide by 0 has no bearing on this problem.

Determine the type of discontinuity this function exhibits.

• jump discontinuity

• none of these

• point discontinuity

• infinite discontinuity

Determine the intervals on which the function f(x) = x³ + x² + x is increasing and the intervals on which the function is decreasing.

• increasing for all x

• increasing for x < 0 and decreasaing for x > 0

• decreasing for all x

• increasing for x < 0 and x > 0

Locate the extrema for the graph of y = f(x).

• The extrema are (-2, 1) and (4, 3).

• The extrema are (-2. 1). (1, -1) and (4, 3).

• The extrema are (-2, 1) and (1, -1).

• The extrema are (-1, 1) and (4, 3).