Absolute Value Functions

Front

What is the definition of an absolute value function?

Back

An absolute value function is a function that outputs the distance of a number from zero on the number line, denoted as f(x) = |x|.

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 |x - a| represent?

Back

The expression |x - a| represents the distance between x and a on the number line.

Front

How do you determine the vertex of an absolute value function in the form f(x) = a|bx + c| + d?

Back

The vertex can be found by solving the equation bx + c = 0 for x, and then substituting that x value into the function to find the corresponding y value.

Front

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

Back

The equation represents a left shift of 3 units and a downward shift of 2 units from the parent function.

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.

Front

What is the effect of multiplying the absolute value function by a positive constant?

Back

Multiplying the absolute value function by a positive constant stretches the graph vertically.

Front

What is the effect of multiplying the absolute value function by a negative constant?

Back

Multiplying the absolute value function by a negative constant reflects the graph across the x-axis and stretches it vertically.