MPT Case Analysis 2

Question 1

A piecewise function is defined as f(x) = 3x + 1 if x < 2, and f(x) = x² - 1 if x ≥ 2. What is f(2) + f(0)?

Accepted Answer

4

Answer

f(2) = 2² - 1 = 3 (x ≥ 2 case), and f(0) = 3(0) + 1 = 1 (x < 2 case), so f(2) + f(0) = 4.

Question 2

Solve the absolute value inequality |2x - 4| > 6 and express as a compound inequality.

Accepted Answer

x < -1 or x > 5

Answer

Split into 2x - 4 > 6 (giving x > 5) or 2x - 4 < -6 (giving x < -1), so x < -1 or x > 5.

Question 3

A function g(x) = |x + 3| - |x - 1|. What is g(-5)?

Accepted Answer

-4

Answer

g(-5) = |-5 + 3| - |-5 - 1| = |-2| - |-6| = 2 - 6 = -4.

Question 4

For what values of x does the piecewise function h(x) = x² if x ≤ 0, and h(x) = 2x if x > 0 satisfy h(x) = 4?

Accepted Answer

x = -2 and x = 2

Answer

For x ≤ 0: x² = 4 gives x = -2 (valid); for x > 0: 2x = 4 gives x = 2 (valid), so both solutions exist.

Question 5

A grading scale assigns A if s ≥ 90, B if 80 ≤ s < 90, and C if 70 ≤ s < 80. Which grade does a score of s = 80 receive?

Accepted Answer

B

Answer

Since 80 ≤ 80 < 90, the score satisfies the B condition.

(MPT) UCF Math Placement Test Practice Test