Absolute Value and Piecewise Functions 24.25

Front

What is the definition of absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |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?

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 adding a constant outside the absolute value have on the graph?

Back

Adding a constant outside the absolute value function shifts the graph vertically. For example, f(x) = |x| + 4 shifts the graph up by 4 units.

Front

What effect does adding a constant inside the absolute value have on the graph?

Back

Adding a constant inside the absolute value function shifts the graph horizontally. For example, f(x) = |x + 2| shifts the graph left by 2 units.

Front

What is the equation of the absolute value function that shifts right by 4 units?

Back

The equation is f(x) = |x - 4|.

Front

How do you find the value of a piecewise function at a specific point?

Back

To find the value of a piecewise function at a specific point, determine which piece of the function applies to that point and evaluate it.

Front

What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions for different intervals of the input variable.

Front

What is the effect of a negative sign in front of an absolute value function?

Back

A negative sign in front of an absolute value function reflects the graph across the x-axis. For example, f(x) = -|x| is a downward-opening V-shape.

Front

How do you graph the function f(x) = 2|x + 2| - 4?

Back

To graph f(x) = 2|x + 2| - 4, start with the parent function |x + 2|, stretch it vertically by a factor of 2, and then shift it down by 4 units.