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Functions Practice Problems with Solutions - IB Year 12

IB Year 12 | Math | Functions
Name: _________________________ Date: _________________________ Score: _______ / 40

f(5) for f(x) = 3x + 2 comes out as 17 and the vertex of y = x² − 4x + 3 is (2, −1), so this IB sheet opens by evaluating functions and completing the square. The key gives x ≥ 3 for a domain and 9 for a later value.

Key Takeaways

Section A: Multiple Choice Questions (1 Mark Each)

Choose the correct option for each question.
1. If f(x) = 3x + 2, find f(5).
(a) 17(b) 13(c) 15(d) 21
2. What is the vertex of y = x² − 4x + 3?
(a) (2, −1)(b) (−1, 2)(c) (2, 1)(d) (−2, −3)
3. What is the domain of f(x) = √(x − 3)?
(a) x ≤ 3(b) x ≥ 3(c) x > 3(d) all real x
4. If f(x) = 2x + 1 and g(x) = x², find f(g(2)).
(a) 8(b) 5(c) 9(d) 16
5. What is the axis of symmetry of y = −2(x − 1)² + 5?
(a) x = 2(b) x = −1(c) x = 1(d) x = 5
6. What is the inverse of f(x) = 2x − 6?
(a) (x − 6) ÷ 2(b) 2x + 6(c) (x + 6) ÷ 2(d) x ÷ 2 − 6

Section B: Short Answer Type Questions (2 Marks Each)

Show all steps clearly.
7. Given f(x) = x² − 5x + 6, find f(0).
8. Find the roots of x² − 5x + 6 = 0.
9. If f(x) = 2x − 3 and g(x) = x², find g(f(2)).
10. State the range of f(x) = x² + 2 for all real x.
11. State the domain of f(x) = 1 ÷ (x − 4).
12. Find the y-intercept of y = 3x − 6.
13. Write the equation of the line through (2, 3) with gradient 4.
14. Solve f(x) = 0 when f(x) = x² − 4.

Section C: Numericals & Word Problems (3 Marks Each)

Apply the concepts to solve the problems. Show all working.
15. A company's cost is C(x) = 50 + 3x dollars for making x units. Find the cost of 40 units.
16. Profit is given by P(x) = −x² + 20x. Find the maximum profit.
17. A ball's height is h(t) = −5t² + 20t + 1 metres. Find the maximum height.
18. A taxi charges $2.50 plus $1.75 per km. Find the fare for a 12 km trip.
19. A car worth $8000 depreciates so that V(t) = 8000 − 500t. After how many years is it worth $0?
20. Revenue is R(x) = x(100 − x). Find the number of units x that maximises revenue.

Answer Key

1. a) 17
2. a) (2, −1)
3. b) x ≥ 3
4. c) 9
5. c) x = 1
6. c) (x + 6) ÷ 2
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
13. Refer to solution guide.
14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet

People Also Ask

What is f(5) when f(x) = 3x + 2?

17, option (a) in this worksheet (Q1).

What is the vertex of y = x² − 4x + 3?

(2, −1), option (a) in this worksheet (Q2).

What is the domain recorded for a later function?

x ≥ 3, option (b) in this worksheet (Q3).

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