Question Type 1: Graphing functions Exercises

Question 1

Sketch the graph of $y = x^2 + 4x + 5$ , labeling the vertex, axis of symmetry, and intercepts; indicate whether there are any $x$ -intercepts.

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Question 2

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

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Question 3

Sketch the graph of $y = -(x-2)^2(x+1)$ , labeling the intercepts and describing the behavior at the double root.

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Question 4

Sketch the graph of $y = x + \dfrac{1}{x}$ , indicating the vertical asymptote, any intercepts, symmetry, and turning points.

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Question 5

Sketch the graph of $y = \dfrac{2x+1}{x-3}$ , labelling the vertical and horizontal asymptotes and the intercepts.

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Question 6

Sketch the graph of $y = (x-2)^2 - 5$ , labeling the vertex, axis of symmetry, and intercepts.

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Question 7

Sketch the graph of $y = -2x + 3$ , labelling the $x$ - and $y$ -intercepts.

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Question 8

Calculate the coordinates of the turning points and sketch the graph of $y = (x-1)(x+2)(x-3)$ , labeling the intercepts and turning points.

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Question 9

Sketch the graph of $y = \dfrac{2}{x-1} + 3$ , labeling the vertical and horizontal asymptotes and the intercepts.

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Question 10

Sketch the graph of $y = \frac{x^2 - 4x + 1}{x - 1}$ , labeling intercepts and the vertical and oblique (slant) asymptotes.

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Question 11

Sketch the graph of $y = \dfrac{x^2 - 1}{x - 1}$ , indicating any discontinuities (asymptotes or holes) and labeling the intercepts.

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Question 12

Sketch the graph of $y = \dfrac{6}{x}$ , labeling the vertical and horizontal asymptotes and indicating any intercepts.

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