NBT NBT Mathematics: Functions and Graphs 5

Question 1

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

Accepted Answer

6

Answer

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

Question 2

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

Accepted Answer

y = (x + 1)(x − 4)

Answer

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

Question 3

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

Accepted Answer

Vertical stretch by factor 3

Answer

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

Question 4

The function f(x) = −3^x is:

Accepted Answer

Always negative

Answer

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

Question 5

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

Accepted Answer

14

Answer

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

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