NBT Mathematics: Functions and Graphs Flashcards

For f(x) = 2x² − 3x + 1, evaluate f(−1).

Answer: 6

f(−1) = 2(1) − 3(−1) + 1 = 2 + 3 + 1 = 6.

The graph of y = f(x) has y-intercept (0, −4) and x-intercepts at x = −1 and x = 4. Which equation is consistent?

Answer: y = (x + 1)(x − 4)

At x = 0: (0+1)(0−4) = −4 ✓. So y = (x+1)(x−4) gives y-intercept −4 and roots −1 and 4.

What transformation maps y = x² onto y = 3x²?

Answer: Vertical stretch by factor 3

Multiplying x² by 3 stretches the graph vertically by a factor of 3.

The function f(x) = −3^x is:

Answer: Always negative

3^x > 0 for all x, so −3^x < 0 for all x — always negative.

A linear function f passes through (−3, 0) and has gradient 2. What is f(4)?

Answer: 14

y = 2(x + 3); f(4) = 2(7) = 14.

The diagram shows g(x) = k · 2^x passing through (2, 12). What is k?

Answer: 3

12 = k · 2² = 4k → k = 3.

For which value of x does 2^x = 1/8?

Answer: x = −3

1/8 = 2^(−3), so 2^x = 2^(−3) → x = −3.