NBT NBT Mathematics: Functions and Graphs 1

Question 1

The function f(x) = 2x − 6. What is the x-intercept?

Accepted Answer

x = 3

Answer

Set f(x) = 0: 2x − 6 = 0 → x = 3.

Question 2

Which graph represents a decreasing linear function with a positive y-intercept?

Accepted Answer

A straight line sloping downward from left to right, crossing the y-axis above the origin

Answer

A decreasing linear function has negative gradient; a positive y-intercept means it crosses the y-axis above zero.

Question 3

The quadratic function g(x) = x² − 4x + 3. What are the roots?

Accepted Answer

x = 1 and x = 3

Answer

Factorise: (x − 1)(x − 3) = 0, giving x = 1 or x = 3.

Question 4

What is the range of f(x) = x² + 1?

Accepted Answer

y ≥ 1

Answer

x² ≥ 0 for all x, so x² + 1 ≥ 1; minimum value is 1.

Question 5

The exponential function h(x) = 3^x. What is h(−2)?

Accepted Answer

1/9

Answer

3^(−2) = 1 ÷ 3² = 1/9.

(NBT) National Benchmark Test Practice Test