Graphs of functions — KCSE Mathematics

KCSE Mathematics · 106 practice questions · 4 syllabus objectives

37 easy36 medium33 hard

What You'll Learn

Key learning outcomes for this topic, aligned to the KNEC KCSE syllabus.

Plot and sketch graphs of linear, quadratic, cubic and reciprocal functions; identify key features (intercepts, turning point, symmetry)

Use graphs to solve equations graphically and read off function values and intercepts

Identify and sketch transformations of graphs: translations (f(x)+a), stretches (af(x)) and reflections (–f(x), f(–x))

Graphs of functions

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easySHORT ANSWER3 marks

State the transformations applied to the graph of y = 2x when it changes to y = 2(x - 3) + 4. (3 marks)

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Part (a) — 3 marks

Translate the graph 3 units to the right (1 mk)

Translate the graph 4 units upward (1 mk)

No change in the shape of the graph; it remains a straight line (1 mk)

easySHORT ANSWER3 marks

Explain how to determine the y-intercept of the function y = -3x + 4 and provide its value. (3 marks)

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Part (a) — 1 mark

The y-intercept is found by setting x = 0 in the function (1 mk)

Part (b) — 2 marks

Substituting x = 0 into the function gives y = 4 (1 mk)

Therefore, the y-intercept is (0, 4) (1 mk)

easySHORT ANSWER2 marks

Define the x-intercept of the function y = 2x + 6 and find its value. (2 marks)

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Part (a) — 1 mark

The x-intercept is the value of x when y = 0 (1 mk)

Part (b) — 1 mark

Set y = 0 and solve: 0 = 2x + 6, leading to x = -3 (1 mk)

Identify the turning point and the line of symmetry for the quadratic function y = -3x² + 6x - 2. (4 marks)

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