Transformation of Absolute Value Functions

Front

What is the parent function of absolute value?

Back

The parent function of absolute value is y = |x|.

Front

How does the equation y = |x + 2| - 5 transform the parent function?

Back

The graph shifts left 2 units and down 5 units.

Front

What effect does a negative sign in front of the absolute value function have?

Back

It reflects the graph across the x-axis.

Front

What does the equation y = -|x| + 6 represent?

Back

It is a downward-opening absolute value function shifted up 6 units.

Front

How do you identify the vertex of the function y = |x - 3| + 2?

Back

The vertex is at the point (3, 2).

Front

What transformation does y = 2|x| represent compared to y = |x|?

Back

It vertically stretches the graph by a factor of 2.

Front

What is the effect of adding a constant outside the absolute value, like in y = |x| + 4?

Back

It shifts the graph up 4 units.

Front

How does the equation y = |x - 1| - 3 transform the parent function?

Back

The graph shifts right 1 unit and down 3 units.

Front

What is the general form of an absolute value function?

Back

The general form is y = a|bx - h| + k, where (h, k) is the vertex.

Front

What does the parameter 'a' in the function y = a|x| do?

Back

The parameter 'a' affects the vertical stretch or compression and the direction of the graph.