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Year 11 Mathematics · Functions and their graphs

Name: ______________________

Date: ____________

1. If f(x) = 3x − 4, what is f(2)?
- ☐ (a) 2
- ☐ (b) −2
- ☐ (c) 10
- ☐ (d) 6
2. Which of these relations is not a function?
- ☐ (a) y = 2x + 1
- ☐ (b) y = x^2
- ☐ (c) x^2 + y^2 = 9
- ☐ (d) y = 5
3. What is the domain of f(x) = sqrt(x + 5)?
- ☐ (a) x ≥ 5
- ☐ (b) x ≥ −5
- ☐ (c) x > 0
- ☐ (d) All real numbers
4. What is the range of y = x^2 − 4?
- ☐ (a) y ≥ 0
- ☐ (b) y ≥ 4
- ☐ (c) All real numbers
- ☐ (d) y ≥ −4
5. How is the graph of y = (x + 2)^2 related to the graph of y = x^2?
- ☐ (a) Moved 2 units right
- ☐ (b) Moved 2 units up
- ☐ (c) Moved 2 units left
- ☐ (d) Moved 2 units down
6. If f(x) = x^2 − 5x, find f(−2).
7. The function g(x) = 1/(x − 3) is defined for all real numbers except one value of x. What is that value?
8. What is the minimum value of y for the function y = (x − 1)^2 + 6?

Answer sheet

1. 2 — f(2) = 3 × 2 − 4 = 6 − 4 = 2.
2. x^2 + y^2 = 9 — x^2 + y^2 = 9 is a circle. For example, x = 0 gives y = 3 and y = −3, so one input has two outputs.
3. x ≥ −5 — We need x + 5 ≥ 0, which gives x ≥ −5.
4. y ≥ −4 — x^2 is never negative, so the smallest value of x^2 − 4 is −4 (when x = 0). The range is y ≥ −4.
5. Moved 2 units left — y = (x + 2)^2 = (x − (−2))^2, so the vertex moves to (−2, 0): 2 units to the left.
6. 14 — f(−2) = (−2)^2 − 5 × (−2) = 4 + 10 = 14.
7. x = 3 — When x = 3 the denominator is 0, and division by zero is undefined.
8. 6 — (x − 1)^2 is never negative and equals 0 when x = 1, so the minimum value of y is 0 + 6 = 6.