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PreCalculus Unit 1 Preassessment

Last updated almost 5 years ago

7 questions

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Question 1

1.

The graph of the function f(x) = x² + x -6 is shown in the coordinate grid.

Which statement(s) describes the graph of f(x)?
I. The graph of f(x) has two zeros.
II. The graph of f(x) has an axis of symmetry at x = -6.25.
III. The point (-1, -5) is on the graph of f(x).
IV. The vertex of the graph of f(x) is located at ( - .5, - 6.25).

A. I only

B. I and III

Question 2

2.

Which of the following represents the domain and range of f(x) = √x + 4?

Domain: {x | x ∈ ℝ, x > 0}  Range: {y | y ∈ ℝ, y > 4}  

Domain: {x | x ∈ ℝ, x ≥ 0}  Range: {y | y ∈ ℝ, y ≥ 4}

Domain: {x | x ∈ ℝ, x ≥ 0}  Range: {y | y ∈ ℝ, y > 4}

Domain: {x | x ∈ ℝ, x > 0}  Range: {y | y ∈ ℝ, y ≥ 4}

Question 3

3.

Which function has a domain of x ≥ -2 ?

y = 4√(x+2) - 2

y = -2√(x+5) - 2

y = 5√(x+4) - 2

y = 3√(x-2) + 2

Question 4

4.

Which statement best describes the asymptotic behavior of the graph of the function f(x) = log (x)

The graph of f(x) = log (x) approaches and crosses the line y = 1.

The graph of f(x) = log (x) approaches and does not cross the line x = 0.

The graph of f(x) = log (x) approaches and does not cross the line y = 0.

The graph of f(x) = log (x) has no asymptotic behavior.

Question 5

5.

Which statement best describes all of the discontinuities for the graph of the function shown below.

The function has a vertical asymptote at x = 4.

The function has a removable discontinuity (hole) at x = -1.

The function has a removable discontinuity (hole) at x = 4 and a vertical asymptote at x = -1.

Question 6

6.

A rational function is shown below.

Which key attribute(s) does the function exhibit?
I. Aymptotes: x = 4, y = -1.
II. Domain: (-∞, - 4) ∪ (- 4, ∞).
III. Range: (-∞, -1] ∪ [-1, ∞).
IV. Rotational symmetry about the point (-4, -1).

I and II only

II, III, and IV only

Question 7

7.

The equation for a rational function is given below.

Which statement represents the type(s) of discontinuity for the rational function?

The function has a removable discontinuity at x = 4 and x = -4.

The function has a vertical asymptote at x = 4 and x = -4.

The graph has a non removable discontinuity at x = -4 and a vertical asymptote at x = 4.

C. II and IV

D. I and IV

The function has a vertical asymptote at x = 4 and a removable discontinuity (hole) at x = -1. 

II and IV only

II and III only

The function has a removable discontinuity at x = 4 and a vertical asymptote at x = -4.