Bluebook SAT Test Linear Functions 5

Question 1

A linear function f satisfies f(3) = 7 and f(7) = 3. What is the value of f(f(5))?

Accepted Answer

5

Answer

The slope is (3 − 7)/(7 − 3) = −1. Using point (3, 7): f(x) = −x + 10. So f(5) = 5, and f(f(5)) = f(5) = 5. The value 5 is a fixed point of the function.

Question 2

The graph of line ℓ is perpendicular to the graph of 4x − 6y = 12 and passes through the point (2, −1). Which of the following is an equation of line ℓ?

Accepted Answer

y = −(3/2)x + 2

Answer

Rewrite 4x − 6y = 12 as y = (2/3)x − 2, giving slope 2/3. A perpendicular slope is −3/2. Through (2, −1): y + 1 = −(3/2)(x − 2) → y = −(3/2)x + 2.

Question 3

The system ax + 2y = 6 and 3x + by = 9 has infinitely many solutions. Which condition must be true?

Accepted Answer

a = 2 and b = 3

Answer

For infinitely many solutions, the equations must be scalar multiples: a/3 = 2/b = 6/9 = 2/3. So a = 2 and b = 3. Check: 2x + 2y = 6 is (2/3) times 3x + 3y = 9 ✓.

Question 4

A table of values for a linear function g is shown: x = −5, −2, 1, 4 and g(x) = 14, 8, 2, −4. What is the value of g(0)?

Accepted Answer

4

Answer

The slope is (8 − 14)/(−2 − (−5)) = −6/3 = −2. Using point (1, 2): g(x) = −2x + 4. Therefore g(0) = 4.

Question 5

A rental company charges a flat hourly rate and a per-mile rate. A customer who drives 12 miles in 3 hours pays $24. Another who drives 20 miles in 2 hours pays $28. What is the per-mile charge?

Accepted Answer

$1.00

Answer

Let a = hourly rate, b = per-mile rate. System: 3a + 12b = 24 and 2a + 20b = 28. Multiply first by 2 and second by 3: 6a + 24b = 48 and 6a + 60b = 84. Subtracting: 36b = 36, so b = $1.00 per mile.

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test Linear Functions 5