Absolute Value Transformations

Front

What is the definition of absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

Front

What is the parent function of absolute value?

Back

The parent function of absolute value is f(x) = |x|.

Front

How does the equation y = |x| + k transform the graph?

Back

It shifts the graph of the parent function up by k units if k is positive and down by k units if k is negative.

Front

What does the equation y = |x - h| represent?

Back

It shifts the graph of the parent function to the right by h units if h is positive and to the left by h units if h is negative.

Front

What is the effect of a negative sign in front of the absolute value, such as in y = -|x|?

Back

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

Front

What transformation does the equation f(x) = |x| - 5 represent?

Back

It shifts the graph of the parent function down by 5 units.

Front

If the equation is f(x) = -|x| + 3, what transformations occur?

Back

The graph is reflected across the x-axis and shifted up by 3 units.

Front

What does the term 'vertical shift' refer to in absolute value transformations?

Back

A vertical shift refers to moving the graph up or down on the coordinate plane.

Front

What does the term 'horizontal shift' refer to in absolute value transformations?

Back

A horizontal shift refers to moving the graph left or right on the coordinate plane.

Front

How do you determine the direction of a shift in the equation y = |x| + b?

Back

If b is positive, the graph shifts up; if b is negative, the graph shifts down.