Absolute Value Graph Transformations

Front

What is the domain of the absolute value function?

Back

(-infinity, infinity)

Front

What is the range of the absolute value function?

Back

[0, infinity)

Front

What does the equation y = |x| represent?

Back

The graph of the absolute value function, which is V-shaped and opens upwards.

Front

How does the graph of y = |x - 3| - 1 transform the basic absolute value graph?

Back

It shifts the graph right 3 units and down 1 unit.

Front

What is the effect of the negative sign in y = -|x|?

Back

It reflects the graph of the absolute value function across the x-axis.

Front

What is the vertex of the graph y = |x - 5| + 2?

Back

The vertex is at the point (5, 2).

Front

How does the graph of y = |x + 4| shift compared to y = |x|?

Back

It shifts left 4 units.

Front

What is the transformation of y = |x| + 3?

Back

It shifts the graph of the absolute value function up 3 units.

Front

What is the effect of multiplying the absolute value function by a factor greater than 1, such as y = 2|x|?

Back

It vertically stretches the graph.

Front

What is the effect of multiplying the absolute value function by a factor between 0 and 1, such as y = 0.5|x|?

Back

It vertically compresses the graph.