Algebra and Functions Flashcards

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

Answer: 1

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

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

Answer: -13

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

Which function has a range of all real numbers?

Answer: f(x) = x³

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.

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

Answer: 21

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

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

Answer: y = f(x + 3) - 2

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

For f(x) = (x + 1)/(x - 1), which value is NOT in the domain of f?

Answer: 1

The denominator x-1 = 0 when x = 1. So x = 1 is excluded from the domain.

If f(x) = 2^x and g(x) = log₂(x), what is f(g(16))?

Answer: 16

g(16) = log₂(16) = 4. f(4) = 2⁴ = 16. f and g are inverses, so f(g(16)) = 16.

The graph of f(x) passes through (0, 3) and (2, 11). If f is linear, what is f(5)?

Answer: 23

Slope = (11-3)/(2-0) = 4. f(x) = 4x+3. f(5) = 20+3 = 23.