Absolute Value Functions

Front

What is the definition of an absolute value function?

Back

An absolute value function is a function that contains an algebraic expression within absolute value symbols, which measures the distance of a number from zero on the number line, always resulting in a non-negative value.

Front

What is the parent function of absolute value?

Back

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

Front

How does the graph of f(x) = |x| look like?

Back

The graph of f(x) = |x| is a V-shaped graph that opens upwards, with its vertex at the origin (0,0).

Front

What effect does a negative sign in front of an absolute value function have?

Back

A negative sign in front of an absolute value function reflects the graph across the x-axis.

Front

What does the expression f(x) = -|x - 2| + 3 represent?

Back

This expression represents an absolute value function that is reflected across the x-axis, shifted right 2 units, and shifted up 3 units.

Front

What is the transformation of the graph f(x) = |x| + 4?

Back

The graph of f(x) = |x| + 4 is the graph of the parent function shifted up 4 units.

Front

What does the term 'compression' mean in the context of absolute value functions?

Back

Compression refers to the vertical shrinking of the graph, making it narrower. For example, f(x) = a|x| where |a| > 1 compresses the graph.

Front

What does the term 'stretch' mean in the context of absolute value functions?

Back

Stretch refers to the vertical stretching of the graph, making it wider. For example, f(x) = a|x| where |a| < 1 stretches the graph.

Front

How do you determine the vertex of the function f(x) = -|x + 1| + 2?

Back

The vertex can be found by identifying the transformation from the parent function. Here, it is shifted left 1 unit and up 2 units, so the vertex is (-1, 2).

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, f(x) = |x| + 3 shifts the graph up 3 units.