Absolute Value and Piecewise Functions

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

How do you graph a piecewise function?

Back

To graph a piecewise function, plot each piece of the function on its specified interval, ensuring to use open or closed dots as needed.

Front

What is the vertex of the function y = a|x - h| + k?

Back

The vertex of the function is the point (h, k), which is the highest or lowest point of the graph depending on the value of 'a'.

Front

What 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 the vertex at the origin (0,0).

Front

What is the effect of changing 'a' in the function y = a|x|?

Back

Changing 'a' affects the vertical stretch or compression of the graph. If 'a' is greater than 1, the graph stretches; if 'a' is between 0 and 1, it compresses.

Front

What is a parent function?

Back

A parent function is the simplest form of a function in a family of functions. For absolute value, the parent function is f(x) = |x|.

Front

How do you find the x-intercepts of the function y = |x - 3|?

Back

To find the x-intercepts, set y = 0: |x - 3| = 0, which gives x = 3.

Front

What is the transformation of the function g(x) = |x + 2|?

Back

The function g(x) = |x + 2| is a horizontal shift of the parent function f(x) = |x| to the left by 2 units.

Front

What does the notation f(x) = -|x| indicate?

Back

The notation f(x) = -|x| indicates a reflection of the parent function across the x-axis.

Front

How do you determine the domain of a piecewise function?

Back

The domain of a piecewise function is the union of the domains of each piece, considering the intervals specified.