Practice Test Geeks(MPT) UCF Math Placement Test Practice Test
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Case Analysis Flashcards

7 cards from real MPT practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 7 Case Analysis flashcards as text

  1. Using case analysis, find all solutions to |x + 2| = |x - 4|.

    Answer: x = 1

    Case 1: x + 2 = x - 4 gives -2 = -4 (impossible); Case 2: x + 2 = -(x - 4) gives 2x = 2, so x = 1.

  2. Analyze cases for the inequality |x - 3| < 2. What is the solution?

    Answer: 1 < x < 5

    |x - 3| < 2 means -2 < x - 3 < 2; adding 3 throughout gives 1 < x < 5.

  3. A piecewise function is f(x) = x + 4 for x ≤ -2, f(x) = x² for -2 < x < 2, and f(x) = 4 - x for x ≥ 2. What is f(-2)?

    Answer: 2

    Since x = -2 satisfies x ≤ -2, use f(x) = x + 4: f(-2) = -2 + 4 = 2.

  4. For x < -1, which expression equals |x + 1| - |x - 1|?

    Answer: -2

    For x < -1: |x+1| = -(x+1) and |x-1| = -(x-1); subtracting gives -(x+1) - (-(x-1)) = -x-1+x-1 = -2.

  5. A taxi charges a $3 base fare plus $2/mile for the first 5 miles and $1.50/mile after that. What is the cost for a 7-mile trip?

    Answer: $16

    First 5 miles: $3 + 5×$2 = $13; remaining 2 miles: 2×$1.50 = $3; total = $13 + $3 = $16.

  6. Determine where f(x) = x/|x| is defined and its value for x > 0.

    Answer: All nonzero reals; 1

    f is undefined at x = 0 (division by zero); for x > 0, |x| = x, so f(x) = x/x = 1.

  7. By case analysis, how many solutions does the equation |2x + 1| = -3 have?

    Answer: 0

    An absolute value is always non-negative, so it can never equal a negative number; there are no solutions.