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|.

Tags

CCSS.6.NS.C.7C

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.

Tags

CCSS.HSF-IF.C.7B

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'.

Tags

CCSS.HSF-IF.C.7D

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).

Tags

CCSS.HSF-IF.C.7D

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.

Tags

CCSS.HSF-IF.C.7D

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.