Absolute Value Transformations

Front

What is the parent function of absolute value?

Back

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

Front

How does a vertical compression affect the graph of an absolute value function?

Back

A vertical compression makes the graph wider, reducing the steepness of the V shape.

Front

What does it mean to shift a graph up or down?

Back

Shifting a graph up means adding a positive constant to the function, while shifting it down means subtracting a constant.

Front

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

Back

A negative sign reflects the graph across the x-axis.

Front

How do you determine the vertex of an absolute value function in the form y = a|x - h| + k?

Back

The vertex is located at the point (h, k).

Front

What does the parameter 'a' represent in the absolute value function y = a|x - h| + k?

Back

The parameter 'a' represents the vertical stretch or compression and the direction of the graph (upward if a > 0, downward if a < 0).

Front

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

Back

The function is shifted down 5 units.

Front

What is the equation of the graph that is vertically compressed by a factor of 2/5 and shifted up 6?

Back

The equation is y = (2/5)|x| + 6.

Front

How does a horizontal shift affect the absolute value function?

Back

A horizontal shift moves the graph left or right, depending on the sign of the constant added or subtracted from x.

Front

What does the transformation f(x) = -|x + 4| + 2 indicate?

Back

This transformation reflects the graph across the x-axis, shifts it left 4 units, and shifts it up 2 units.