Quick questions on Absolute value functions - TCE Mathematics Specialised (Tasmania)

Q: What is sketching the basic graph?

The graph of y = |x| is a V shape with its vertex at the origin, made of the line y = x for x 0 and the line y = -x for x < 0. Transformations work just like any function: y = |x - 2| + 1 shifts the V two units right and one unit up, so its vertex sits at (2, 1).

Q: What are solving absolute value equations?

To solve |f(x)| = a (with a 0), the inside can be either +a or -a:

2short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is sketching the basic graph?

Show answer

The graph of

y = |x|

is a V shape with its vertex at the origin, made of the line

y = x

for

x \ge 0

and the line

y = -x

for

x < 0

. Transformations work just like any function:

y = |x - 2| + 1

shifts the V two units right and one unit up, so its vertex sits at

(2, 1)

What are solving absolute value equations?

Show answer

To solve

|f(x)| = a

(with

a \ge 0

), the inside can be either

+a

-a

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