11.8.A.1Multiple Choice
What are the real zeros of r(x) = (x − 5)(x + 1)/(x − 2)?
Select A, B, C, or D to check your answer.
Directions: Work each problem on your own paper first. For multiple choice, select A, B, C, or D. You will see right away whether you are correct. If you miss, you will see the most likely reason, and you can try again. For short response, type your answer, then compare it with the model solution. Questions 1–7 cover 1.8.A.1; 8–19 cover 1.8.A.2; question 20 covers both.
What are the real zeros of r(x) = (x − 5)(x + 1)/(x − 2)?
Select A, B, C, or D to check your answer.
What are the real zeros of r(x) = (3x² − 12)/(x² + 4)?
Select A, B, C, or D to check your answer.
What are the real zeros of r(x) = 7/(x + 1)?
Select A, B, C, or D to check your answer.
Let r(x) = (2x² − 5x − 3)/(x − 4). (a) Factor the numerator. (b) Find all real zeros of r. (c) Which input is not in the domain of r, and why is it not a zero? (d) Find r(0).
Which statement is true about the real zeros of r(x) = (x² − 9)/(x + 3)?
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The graph of a rational function r is shown. It crosses the x-axis at x = −2 and x = 3, and the dashed line marks a zero of the denominator at x = 1. Which of the following could be r(x)?
Select A, B, C, or D to check your answer.
Which of the following functions has exactly one real zero?
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Let r(x) = (x − 1)(x + 3)/(x − 2). (a) List the critical values and say which are zeros of the numerator and which are zeros of the denominator. (b) Choose a test point in each interval and give the sign of r there. (c) Solve r(x) ≥ 0. (d) Explain why x = 2 is never part of the solution.
Solve r(x) > 0 for r(x) = (x + 2)(x − 4)/(x + 1).
Select A, B, C, or D to check your answer.
Solve r(x) ≤ 0 for r(x) = x/(x − 5).
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For r(x) = (x + 1)(x − 4)/(x − 2), the critical values are −1, 2, and 4. Which list gives the sign of r on the intervals (−∞, −1), (−1, 2), (2, 4), (4, ∞), in that order?
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Solve r(x) ≥ 0 for r(x) = (x − 3)²/(x + 1).
Select A, B, C, or D to check your answer.
Let r(x) = (x − 4)/(x + 1)². (a) List the critical values, with type (numerator or denominator) and multiplicity. (b) Find the sign of r on each interval. (c) Solve r(x) ≥ 0. (d) Solve r(x) < 0.
The graph of r(x) = (x − 1)(x + 2)/((x + 4)(x − 3)) is shown. The x-intercepts are at −2 and 1, and the dashed lines are at x = −4 and x = 3. Which is the solution of r(x) ≤ 0?
Select A, B, C, or D to check your answer.
Solve r(x) ≥ 0 for r(x) = (x − 1)/(x + 3).
Select A, B, C, or D to check your answer.
Solve r(x) > 0 for r(x) = 5/(x + 2)².
Select A, B, C, or D to check your answer.
Let r(x) = (x + 2)²(x − 1)/(x − 4). (a) List the critical values with type and multiplicity. (b) Test a point in each interval and give the sign of r. (c) Solve r(x) ≤ 0. (d) Does the sign change at x = −2? Explain using multiplicity.
Which statement about the solution of r(x) ≤ 0 for a rational function r is always true?
Select A, B, C, or D to check your answer.
For r(x) = (x + 3)(x − 1)(x − 6)/((x + 1)(x − 4)), how many intervals do the critical values cut the number line into?
Select A, B, C, or D to check your answer.
Let r(x) = (x − 3)(x + 5)/(x + 1)². (a) Find the real zeros of r and any input that is not in the domain. (b) List the critical values with type and multiplicity. (c) Find the sign of r on each interval and solve r(x) > 0. (d) Solve r(x) ≤ 0.