NBT Mathematics Functions and Calculus

Question 1

What is the domain of f(x) = √(4 − x)?

Accepted Answer

x ≤ 4

Answer

For the square root to be defined, the expression inside must be non-negative: 4 − x ≥ 0 gives x ≤ 4.

Question 2

What is the derivative of f(x) = 3x² − 2x + 5?

Accepted Answer

6x − 2

Answer

Using the power rule: the derivative of 3x² is 6x, the derivative of −2x is −2, and constants vanish, giving 6x − 2.

Question 3

What is lim(x→2) [(x² − 4) / (x − 2)]?

Accepted Answer

4

Answer

Factoring gives (x+2)(x−2)/(x−2) = x+2; substituting x=2 yields 4.

Question 4

If f(x) = 2x + 1 and g(x) = x², what is f(g(3))?

Accepted Answer

19

Answer

g(3) = 9, then f(9) = 2(9) + 1 = 19.

Question 5

The range of f(x) = −x² + 3 is:

Accepted Answer

y ≤ 3

Answer

The parabola opens downward with vertex at (0, 3), so the maximum output is 3 and f(x) ≤ 3 for all x.

National Benchmark Test (NBT) Practice Test