1B Piecewise and Absolute Value Function

Front

What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions or formulas for different parts of its domain.

Front

What is the absolute value of a number?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always non-negative.

Front

How does the graph of y = |x| look?

Back

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

Front

What transformation occurs in the equation y = |x + 3|?

Back

The graph of y = |x + 3| is shifted 3 units to the left.

Front

What transformation occurs in the equation y = |x| - 2?

Back

The graph of y = |x| - 2 is shifted 2 units down.

Front

How do you find f(-3) for a piecewise function?

Back

To find f(-3), determine which piece of the function applies when x = -3 and evaluate that expression.

Front

What does the notation |x| represent?

Back

The notation |x| represents the absolute value of x.

Front

If f(x) = |x - 1|, what is f(1)?

Back

f(1) = |1 - 1| = |0| = 0.

Front

What is the domain of the function f(x) = |x|?

Back

The domain of f(x) = |x| is all real numbers, (-∞, ∞).

Front

What is the range of the function f(x) = |x|?

Back

The range of f(x) = |x| is all non-negative real numbers, [0, ∞).