Bluebook SAT Test Linear Functions 6 — Questions and Answers
Question 1: A company's weekly profit P (in dollars) is modeled by P(u) = 45u − 360, where u is the number of units sold. How many units must be sold for the company to break even (P = 0)?
- 4
- 6
- 8 (Correct answer)
- 10
Correct answer: 8
Set P = 0: 45u − 360 = 0 → 45u = 360 → u = 8 units.
Question 2: If f(x) = −5x + 2 and g(x) = 3x − 6, for what value of x does f(x) = g(x)?
- −1
- 0
- 1 (Correct answer)
- 2
Correct answer: 1
−5x + 2 = 3x − 6 → 8 = 8x → x = 1.
Question 3: The linear model T = 0.9F − 17.8 converts a temperature in degrees Fahrenheit (F) to a temperature in Celsius (T). Approximately what Fahrenheit temperature corresponds to 0°C?
- 0°F
- 18°F
- 20°F (Correct answer)
- 32°F
Correct answer: 20°F
Set T = 0: 0 = 0.9F − 17.8 → 0.9F = 17.8 → F ≈ 19.8 ≈ 20°F.
Question 4: Point A is at (0, 3) and point B is at (6, 0). What is the length of segment AB?
- 3√3
- 3√5 (Correct answer)
- 6
- 9
Correct answer: 3√5
AB = √((6−0)² + (0−3)²) = √(36 + 9) = √45 = 3√5.
Question 5: A linear function f has the following values: f(1) = 4 and f(4) = 13. What is the slope of f?
- 2
- 3 (Correct answer)
- 4
- 5
Correct answer: 3
Slope = (13 − 4)/(4 − 1) = 9/3 = 3.
Question 6: Which equation represents a line that passes through (2, −3) with slope 1/2?
- y = (1/2)x − 4 (Correct answer)
- y = (1/2)x + 2
- y = 2x − 3
- y = (1/2)x − 1
Correct answer: y = (1/2)x − 4
Using point-slope form: y − (−3) = (1/2)(x − 2) → y = (1/2)x − 1 − 3 = (1/2)x − 4.
Question 7: For the linear function shown in the table, what is the missing value? x: 1 2 3 4 f: 6 9 12 ?
- 13
- 14
- 15 (Correct answer)
- 16
Correct answer: 15
The common difference is 3, so f(4) = 12 + 3 = 15.
Bluebook SAT Test Linear Functions 6
A company's weekly profit P (in dollars) is modeled by P(u) = 45u − 360, where u is the number of units sold.
How many units must be sold for the company to break even (P = 0)?