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 \(f(x) = 2x^3 - x^2 + 4\). Compute \(f(2)\). 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: \(V(t) = 50 \cdot 2^t\) (in TB). How many TB after \(6\) years? 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 \(f^{-1}(x)\)?

11. Let \(f(x) = 2x + 1\) and \(g(x) = x^2\). Compute \((f \circ g)(3)\). Type the number.

12. “Every function has an inverse.” True or false? Type one word, lowercase.

Well done. You solved every question. You can evaluate functions, recognize the gallery types, find maximal domains, and handle composition and inverses. You are ready for Session 04 on differentiation.