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, 'a' is the vertical stretch/compression, and 'b' affects the horizontal stretch/compression.

Front

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

Back

A vertical stretch by a factor of 'a' (where a > 1) makes the graph narrower, while a vertical compression (0 < a < 1) makes it wider.

Front

What does a horizontal shift to the left by 'h' units look like in an absolute value function?

Back

The function takes the form f(x) = |x + h|, shifting the graph left by 'h' units.

Front

How does a vertical shift down by 'k' units affect the graph of an absolute value function?

Back

The function takes the form f(x) = |x| - k, shifting the graph down by 'k' units.

Front

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

Back

The function takes the form f(x) = -|x|, inverting the graph over the x-axis.

Front

What is the vertex of the absolute value function f(x) = a|bx - h| + k?

Back

The vertex is the point (h, k) in the coordinate plane.

Front

How do you determine the vertex of the function y = 4|x| + 1?

Back

The vertex is at (0, 1) since it is in the form f(x) = a|x| + k with a = 4 and k = 1.

Front

What transformations are applied to the function f(x) = |x| to obtain f(x) = 2|x + 1| - 9?

Back

A vertical stretch by 2, a horizontal shift left by 1 unit, and a vertical shift down by 9 units.

Front

What does the notation |–2x + 6| represent in terms of transformations?

Back

It represents a reflection across the x-axis, a vertical stretch by a factor of 2, and a horizontal shift.

Front

How do you write the equation of an absolute value function given its vertex?

Back

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