Worksheet · solutions includedFunction Evaluation & Asymptotes — Practice Worksheet
Try each problem first, then click Show solution. To print an answer key, open all solutions before File ▸ Print.
Section A — the questions you missed
Original — Math M2 Q6 (you answered B; correct C)
The function f is defined by f(x) = (x + 15)/5, and f(a) = 10, where a is a constant. What is a?
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(a + 15)/5 = 10 → a + 15 = 50 → a = 35.
Answer: C) 35
Original — Math M2 Q18 (you answered B; correct C)
A curve is in quadrant 3, trending down sharply. As x increases it approaches the line x = −4; as x decreases it approaches y = 0. Which equation could define the curve?
- A.y = 1/(x − 4)
- B.y = 1/x − 4
- C.y = −1/(x + 4)
- D.y = −1/x + 4
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Vertical asymptote at x = −4 → denominator (x + 4). Eliminates A, B, D.
Horizontal asymptote y = 0 (no constant added) matches C.
The negative sign puts the relevant branch in quadrant 3.
Answer: C) y = −1/(x + 4)
Section B — new practice (same skills)
Practice 1
f(x) = (2x − 6)/4 and f(a) = 5. Find a.
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(2a − 6)/4 = 5 → 2a − 6 = 20 → 2a = 26 → a = 13.
Answer: 13
Practice 2
g(x) = 3x2 − x + 2. What is g(−2)?
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3(−2)2 − (−2) + 2 = 12 + 2 + 2 = 16.
Answer: 16
Practice 3
A rational function has a vertical asymptote at x = 3 and a horizontal asymptote at y = 0. Which could it be: y = 1/(x−3), y = 1/(x+3), or y = 1/x + 3?
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Vertical asymptote at x = 3 → denominator (x − 3).
Horizontal asymptote y = 0 → no added constant.
So y = 1/(x − 3).
Answer: y = 1/(x − 3)
Practice 4
h(x) = (x + 1)/(x − 2). For large x, what value does h approach?
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Ratio of leading coefficients = 1/1 = 1.
Horizontal asymptote y = 1.
Answer: 1