NBT Mathematics: Functions and Graphs Flashcards

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

Answer: x = 3

Set f(x) = 0: 2x − 6 = 0 → x = 3.

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

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

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

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

Answer: x = 1 and x = 3

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

What is the range of f(x) = x² + 1?

Answer: y ≥ 1

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

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

Answer: 1/9

3^(−2) = 1 ÷ 3² = 1/9.

For the parabola y = −2(x − 1)² + 8, what is the maximum value of y?

Answer: 8

The vertex is at (1, 8); since the coefficient is negative, y = 8 is the maximum.

A graph of y = f(x) shows that f(2) = 5 and f(5) = −1. What is the average rate of change between x = 2 and x = 5?

Answer: −2

Average rate = (f(5) − f(2)) ÷ (5 − 2) = (−1 − 5) ÷ 3 = −6/3 = −2.