Exercises for Question Type 1: Graphing equations with the absolute value of the whole function

Question 1

Skill question

Sketch the graph of $y = ∣ x^{2} - 5 x - 6∣$ .

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Question 2

Skill question

Find the domain and range of $y = ∣ x^{2} - 5 x - 6∣$ .

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Question 3

Skill question

Solve the equation $∣ x^{2} - 5 x - 6∣ = 4$ .

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Question 4

Skill question

Determine the coordinates of the local maximum point on the graph of $y = ∣ x^{2} - 5 x - 6∣$ .

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Question 5

Skill question

Find the $x$ -intercepts of $y = ∣ x^{2} - 5 x - 6∣$ .

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Question 6

Skill question

Sketch the graph of $y = 3 x^{2} - 5 x - 6$ and state the effect compared to $y = ∣ x^{2} - 5 x - 6∣$ .

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Question 7

Skill question

Find the minimum value of $f (x) = ∣ x^{2} - 5 x - 6∣$ and the values of $x$ at which it occurs.

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Question 8

Skill question

Determine the intervals on which $f (x) = ∣ x^{2} - 5 x - 6∣$ is increasing and decreasing.

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Question 9

Skill question

Sketch the graph of $y = ∣ x^{2} - 5 x - 6∣ - 2$ and describe its transformation from $y = ∣ x^{2} - 5 x - 6∣$ .

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Question 10

Skill question

Solve the inequality $∣ x^{2} - 5 x - 6∣ \leq 9$ .

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Question 11

Skill question

For what values of $k$ does the graph $y = ∣ x^{2} - 5 x - 6∣ + k$ intersect the $x$ -axis at exactly two points?

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Question 12

Skill question

Express $y = ∣ x^{2} - 5 x - 6∣$ as a piecewise-defined function.

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IB Mathematics Analysis and Approaches Question Type 1: Graphing Equations with the Absolute Value of the Whole Function Exercises