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.

Tags

TEKS.MATH.6.2B

Front

What is the parent function of absolute value?

Back

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

Tags

TEKS.MATH.AR.3A

TEKS.MATH.AR.7B

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.

Tags

TEKS.MATH.2A.6C

Front

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

Back

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

Tags

TEKS.MATH.2A.6C

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.

Tags

TEKS.MATH.2A.6C

Front

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

Back

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

Tags

TEKS.MATH.2A.6C

Front

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

Back

It represents a vertical shift upward by k units.

Tags

TEKS.MATH.2A.6C

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.

Tags

TEKS.MATH.2A.6C

Front

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

Back

It shifts the graph vertically.

Tags

TEKS.MATH.2A.6C

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).

Tags

TEKS.MATH.2A.6C