Transformations of Absolute Value Functions

Front

What is the general form of an absolute value function?

Back

y = a|bx - h| + k, where (h, k) is the vertex, 'a' affects the width and direction, and 'b' affects the horizontal stretch.

Front

How does the value of 'a' in the absolute value function affect the graph?

Back

'a' determines the width and direction of the graph. If |a| > 1, the graph is narrow; if 0 < |a| < 1, the graph is wide. If 'a' is negative, the graph is flipped.

Front

What does it mean for an absolute value function to be 'shifted up'?

Back

The entire graph moves vertically upwards by adding a positive value to 'k' in the equation y = a|bx - h| + k.

Front

What does it mean for an absolute value function to be 'shifted down'?

Back

The entire graph moves vertically downwards by subtracting a value from 'k' in the equation y = a|bx - h| + k.

Front

How does the term (x - h) in the absolute value function affect the graph?

Back

It shifts the graph horizontally. If h is positive, the graph shifts to the right; if h is negative, it shifts to the left.

Front

What is the effect of adding a constant outside the absolute value function?

Back

Adding a constant outside the absolute value function shifts the graph vertically. For example, y = |x| + 3 shifts the graph up by 3 units.

Front

What is the effect of subtracting a constant outside the absolute value function?

Back

Subtracting a constant outside the absolute value function shifts the graph vertically down. For example, y = |x| - 2 shifts the graph down by 2 units.

Front

What does it mean for an absolute value function to be 'flipped'?

Back

A flipped graph occurs when 'a' is negative in the function y = a|bx - h| + k, resulting in the graph opening downwards.

Front

How do you determine if an absolute value function is wide or narrow?

Back

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

Front

What is the vertex of the absolute value function y = a|bx - h| + k?

Back

The vertex is the point (h, k), which is the highest or lowest point of the graph depending on the value of 'a'.