Exercises for Question Type 1: Graphing equations with the absolute value of the whole function - IB | RevisionDojo

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

Question 1

Sketch the graph of $y = |x^2 - 5x - 6|$ .

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Question 2

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

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Question 3

Solve the equation $|x^2 - 5x - 6| = 4$ .

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Question 4

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

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Question 5

Find the $x$ -intercepts of $y = |x^2 - 5x - 6|$ .

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Question 6

Sketch the graph of $y = 3\bigl|x^2 - 5x - 6\bigr|$ and state the effect compared to $y=|x^2 - 5x - 6|$ .

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Question 7

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

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Question 8

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

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Question 9

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

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Question 10

Solve the inequality $|x^2 - 5x - 6| \le 9$ .

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Question 11

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

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Question 12

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

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