Graphing techniques

Transform and verify the whole curve · Diagrams · Complete reading

From a line to absolute value

Compare the original graph with its absolute value. The input stays the same; only negative outputs are reflected upwards.

Start: Original graph

y=x

First identify the zeros and the parts above and below the x-axis.

Marked points at this step, rounded to 6 significant figures.
Point	x	y
O	0	0

Ideas to try

Choose Step 1, then compare with Start. Which part of the graph changes?
Open Point coordinates to check that the zeros stay fixed. Hide the comparison to inspect the final graph.

Source line y=x and reflected V y=|x| over x−3..3; negative original segment dashed; final panel labels y=−x for x<0 and y=x for x≥0.

Open original diagram

Reflect only the negative quadratic section

Compare the original graph with its absolute value. The input stays the same; only negative outputs are reflected upwards.

Start: Original graph

y=x^2-3x+2

First identify the zeros and the parts above and below the x-axis.

Marked points at this step, rounded to 6 significant figures.
Point	x	y
(0, 2)	0	2
1	1	0
2	2	0

Ideas to try

Choose Step 1, then compare with Start. Which part of the graph changes?
Open Point coordinates to check that the zeros stay fixed. Hide the comparison to inspect the final graph.

Source quadratic x²−3x+2 with roots 1,2 and y-intercept 2; absolute-value curve reflects only its negative section between 1 and 2, showing the original arc dashed.

Open original diagram

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