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Worked solution

Sketch the modulus of a shifted straight line

Given f(x)=x+4f(x)=x+4, sketch y=∣f(x)∣y=|f(x)|.

CJC · Transformations · Self-Practice 5

Sketch the two straight-line pieces

Answer

y=∣x+4∣y=|x+4|, with vertex (−4,0)(-4,0) and y-intercept (0,4)(0,4).

Independently derived: use y=x+4y=x+4 for x≥−4x\ge-4, and y=−x−4y=-x-4 for x<−4x<-4. Reflect only the portion below the x-axis. Neither copy prints a self-practice answer on this page.

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Independently derived V-shaped graph |x+4|, vertex (−4,0), y-intercept (0,4), slopes −1 to the left of −4 and 1 to the right.
Independently derived V-shaped graph |x+4|, vertex (−4,0), y-intercept (0,4), slopes −1 to the left of −4 and 1 to the right.
Independently derived V-shaped graph |x+4|, vertex (−4,0), y-intercept (0,4), slopes −1 to the left of −4 and 1 to the right.
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