Absolute Value Equations Transformations

Front

What is the parent function of absolute value?

Back

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

Front

What transformation is applied in the function f(x) = |x| - 5?

Back

The function shifts down 5 units.

Front

What does the equation f(x) = 4|x - 3| represent?

Back

It represents an absolute value function that is vertically stretched by a factor of 4 and shifted right 3 units.

Front

How do you write the equation for a vertically compressed absolute value function by a factor of 2/5 and shifted up 6?

Back

The equation is y = \frac{2}{5}|x| + 6.

Front

What is the effect of a negative sign in front of an absolute value function?

Back

It reflects the graph over the x-axis.

Front

What does a horizontal shift to the right by 2 units look like in an absolute value function?

Back

The function becomes f(x) = |x - 2|.

Front

How do you express a vertical shift down 7 units in an absolute value function?

Back

The function becomes f(x) = |x| - 7.

Front

What is the equation for an absolute value function that is reflected over the x-axis, shifted right 2 units, and down 7 units?

Back

The equation is y = -|x - 2| - 7.

Front

What does the term 'vertical compression' mean in the context of absolute value functions?

Back

Vertical compression means the graph is squeezed towards the x-axis, making it less steep.

Front

What is the effect of a vertical stretch on the graph of an absolute value function?

Back

A vertical stretch makes the graph steeper.