Question Type 1: Graphing functions Exercises

Question 1

Sketch the graph of $y = 2x - 4$ . Show the $x$ - and $y$ -intercepts and the gradient.

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Question 2

Sketch the graph of $y = \dfrac{6}{x-2}$ . Show the asymptotes and intercepts, and indicate the branches.

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Question 3

Sketch the graph of $y = x^2 - 5x + 4$ . Show the vertex, intercepts, and axis of symmetry.

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Question 4

Sketch the graph of $y = \dfrac{3x - 6}{x + 2}$ . Show the vertical and horizontal asymptotes and the intercepts.

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Question 5

Sketch the graph of $y = \dfrac{x^2-1}{x-1}$ . Identify any discontinuities and key features.

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Question 6

Sketch the graph of $y = \dfrac{x^2}{x-1}$ . Show intercepts, vertical and oblique asymptotes, and indicate which side of the oblique asymptote the curve lies for large $|x|$ .

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Question 7

Sketch the graph of $y = (x+1)(x-2)^2$ . Show the intercepts, behavior at each root, and end behavior.

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Question 8

Sketch the graph of $y = (x-3)^2 - 4$ . Show the vertex, axis of symmetry, and intercepts.

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Question 9

Sketch the graph of $y = \dfrac{x+1}{x-3}$ . Show the vertical and horizontal asymptotes and the intercepts.

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Question 10

Sketch the graph of $y = x^3 - 3x$ . Show all intercepts, stationary points, and the nature of each stationary point.

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Question 11

Sketch the graph of $y = |2x - 6| - 4$ . Show the vertex and intercepts.

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Question 12

Sketch the graph of $y = \sqrt{x+2} - 1$ . Indicate the domain and intercepts.

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