Transformation of Absolute Value Functions

Front

What is the general form of an absolute value function?

Back

f(x) = a|bx - h| + k, where (h,k) is the vertex.

Front

What does the parameter 'a' in the absolute value function affect?

Back

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

Front

How does a positive 'h' value in f(x) = |x - h| affect the graph?

Back

It shifts the graph to the right by 'h' units.

Front

How does a negative 'h' value in f(x) = |x - h| affect the graph?

Back

It shifts the graph to the left by 'h' units.

Front

What effect does a positive 'k' value have on the graph of an absolute value function?

Back

It shifts the graph upward by 'k' units.

Front

What effect does a negative 'k' value have on the graph of an absolute value function?

Back

It shifts the graph downward by 'k' units.

Front

What is the vertex of the function y = |x|?

Back

The vertex is at the point (0,0).

Front

How do you determine the width of an absolute value function compared to its parent function?

Back

The width is determined by the value of 'a': if |a| > 1, the graph is narrow; if |a| < 1, the graph is wide.

Front

What is the effect of reflecting an absolute value function across the x-axis?

Back

It changes the function to f(x) = -|x|, flipping it upside down.

Front

What is the vertex of the function y = 3|x - 2| + 1?

Back

The vertex is at the point (2,1).