Absolute Value Functions

Front

What is the definition of absolute value?

Back

The absolute value of a number is the distance the number is from zero on the number line, regardless of direction.

Front

What is the parent function of absolute value?

Back

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

Front

Describe the transformation of the function f(x) = 3|x + 4| - 5 compared to the parent function f(x) = |x|.

Back

The function is more narrow, shifted left 4 units, and down 5 units.

Front

What effect does a negative coefficient have on an absolute value function?

Back

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

Front

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

Back

If |a| > 1, the graph is narrower; if 0 < |a| < 1, the graph is wider.

Front

What does the expression |x - h| represent in terms of transformations?

Back

It represents a horizontal shift to the right by h units.

Front

What does the expression |x| + k represent in terms of transformations?

Back

It represents a vertical shift upward by k units.

Front

If f(x) = -|x| + 2, what transformations are applied to the parent function?

Back

The graph is reflected over the x-axis and shifted up 2 units.

Front

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

Back

It shifts the graph vertically.

Front

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

Back

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