Self-Test 03 - Functions

Check your understanding

This self-test lets you check your understanding of Session 03. It is purely formative: nothing is tracked or graded, and nobody sees your answers. Work through the Tasks first, then use this quiz to confirm the ideas have stuck. A wrong answer triggers a 10-second cooldown before you can retry, so think before you click.

1. Let \(f(x) = x^2 - 3x\). What is \(f(-2)\)?

2. Which equation does NOT define \(y\) as a function of \(x\)?

3. Let \(f: \mathbb{R} \to \mathbb{R}\), \(f(x) = (x - 3)^2 + 2\). What is the smallest number in the range of \(f\)? Type the number.

Function Gallery

4. A courier’s total cost rises by the same amount for each additional parcel. Which function type models this?

5. Consider \(f(x) = 5 \cdot 2^x\). Which statement is true?

6. A company’s data volume doubles every year: \(W(t) = 50 \cdot 2^t\) (in TB). After how many years does it reach \(3200\) TB? Type the number.

Maximal Domain

7. What is the maximal domain of \(f(x) = \dfrac{\sqrt{x + 3}}{x - 1}\)?

8. How many real numbers are excluded from the maximal domain of \(f(x) = \dfrac{x + 4}{x^2 - 9}\)? Type the number.

Composition & Inverses

9. Let \(f(x) = x^2\) and \(g(x) = x - 3\). What is \((f \circ g)(x)\)?

10. Let \(f(x) = 4x\). What is the inverse function \(f^{-1}(x)\)?

Properties

11. Which of these business functions is concave on the given domain?

12. The roastery’s revenue is \(R(p) = 1200p - 20p^2\). Which other price gives the same revenue as \(p = 20\)? Type the number.

Well done. You solved every question. You can evaluate functions, recognise the gallery types, find ranges and maximal domains, handle composition and inverses, and read a function’s shape. You are ready for Session 04 on differentiation.