Porisma

Worked solution

Sketch a shifted input-modulus graph

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

CJC · Transformations · Self-Practice 6

Retain and mirror the non-negative input half

Answer

y=∣x∣+4y=|x|+4, with vertex (0,4)(0,4) and no x-intercept.

Independently derived: use y=x+4y=x+4 for x≥0x\ge0 and y=−x+4y=-x+4 for x<0x<0. Retain the right-hand half of the original line and reflect it in the y-axis. This differs from ∣x+4∣|x+4|, whose vertex is (−4,0)(-4,0). Neither copy prints a self-practice answer on this page.

Expand diagram

Use the scrollbars or arrow keys to inspect details.

Independently derived V-shaped graph |x|+4, symmetric about the y-axis, vertex (0,4), range y≥4 and no x-intercept.
Independently derived V-shaped graph |x|+4, symmetric about the y-axis, vertex (0,4), range y≥4 and no x-intercept.
Independently derived V-shaped graph |x|+4, symmetric about the y-axis, vertex (0,4), range y≥4 and no x-intercept.
How did this part go?