Bluebook SAT Test Algebra and Functions 2

Question 1

If f(x) = 4 - x² and g(x) = 2x, what is (f + g)(3)?

Accepted Answer

1

Answer

f(3) = 4-9 = -5. g(3) = 6. (f+g)(3) = -5+6 = 1.

Question 2

The linear function f satisfies f(0) = 5 and f(3) = -1. What is f(9)?

Accepted Answer

-13

Answer

Slope = (-1-5)/(3-0) = -2. f(x) = -2x+5. f(9) = -18+5 = -13.

Question 3

Which function has a range of all real numbers?

Accepted Answer

f(x) = x³

Answer

x³ can produce any real number as output (range = all reals). x² only produces non-negatives, √x only non-negatives, and 1/x cannot produce 0.

Question 4

If f(2x + 1) = 4x² + 4x - 3, what is f(5)?

Accepted Answer

21

Answer

Set 2x+1=5: x=2. f(5) = 4(4)+4(2)-3 = 16+8-3 = 21.

Question 5

The graph of y = f(x) is shifted 3 units left and 2 units down. Which equation represents the new graph?

Accepted Answer

y = f(x + 3) - 2

Answer

Shifting left by 3 replaces x with (x+3). Shifting down by 2 subtracts 2. Result: y = f(x+3) - 2.

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