Bluebook SAT Test Linear Functions 10 — Questions and Answers
Question 1: A candle is 18 cm tall and burns at 0.6 cm per minute. The function h(t) = 18 − 0.6t models its height. After how many minutes will it be 7.2 cm tall?
- 18 (Correct answer)
- 12
- 9
- 15
Correct answer: 18
18 − 0.6t = 7.2 → 0.6t = 10.8 → t = 18.
Question 2: Line r is perpendicular to y = (3/4)x − 2. Which equation could represent line r?
- y = −(4/3)x + 5 (Correct answer)
- y = (3/4)x + 5
- y = (4/3)x + 5
- y = −(3/4)x + 5
Correct answer: y = −(4/3)x + 5
The perpendicular slope is the negative reciprocal of 3/4, which is −4/3; y = −(4/3)x + 5 has that slope.
Question 3: If g(x) = −3x + 7, for what value of x does g(x) = g(−1)?
- −1 (Correct answer)
- 1
- 0
- 2
Correct answer: −1
g(−1) = −3(−1) + 7 = 10; g(x) = 10 → −3x + 7 = 10 → −3x = 3 → x = −1. The function value g(−1) equals itself only at x = −1.
Question 4: Two lines intersect at (3, 5). One line has equation y = x + 2. Which of the following could be the other line's equation?
- y = −2x + 11 (Correct answer)
- y = 2x − 1
- y = x − 2
- y = −x + 2
Correct answer: y = −2x + 11
Check: −2(3) + 11 = −6 + 11 = 5 ✓; (3, 5) lies on y = −2x + 11.
Question 5: What does the x-intercept of a linear function represent in a context where y is profit (in dollars) and x is units sold?
- The break-even point — the number of units where profit equals zero (Correct answer)
- The starting profit before any units are sold
- The rate of profit increase per unit
- The maximum profit achievable
Correct answer: The break-even point — the number of units where profit equals zero
The x-intercept is where profit y = 0, meaning the number of units at which the business neither gains nor loses money — the break-even point.
Question 6: The table below shows a linear function. What is the missing value? x: −1, 0, 1, 2 | y: −5, −2, 1, ?
- 4 (Correct answer)
- 3
- 5
- 2
Correct answer: 4
The rate of change is 3 per unit; continuing from y = 1 at x = 1: y = 1 + 3 = 4.
Question 7: A swimmer starts 200 meters from a dock and swims toward it at 2.5 meters per second. Which function models distance d from the dock after t seconds?
- d(t) = 200 − 2.5t (Correct answer)
- d(t) = 200 + 2.5t
- d(t) = 2.5t − 200
- d(t) = 2.5t + 200
Correct answer: d(t) = 200 − 2.5t
Starting at 200 m and decreasing at 2.5 m/s gives d(t) = 200 − 2.5t.
Question 8: For f(x) = 5x − 9 and g(x) = 3x + 1, what is the x-value where f(x) = g(x)?
- 5 (Correct answer)
- −5
- 2
- −2
Correct answer: 5
5x − 9 = 3x + 1 → 2x = 10 → x = 5.
Bluebook SAT Test Linear Functions 10
A candle is 18 cm tall and burns at 0.6 cm per minute.
The function h(t) = 18 − 0.6t models its height.
After how many minutes will it be 7.2 cm tall?