4.4 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 find the minimum of a piecewise function?

Back

To find the minimum of a piecewise function, evaluate each piece at its defined intervals and compare the values to determine the lowest point.

Front

What is the vertex of the function f(x) = |x - h| + k?

Back

The vertex of the function is the point (h, k), which represents the minimum point of the graph if k is the lowest value.

Front

Describe the transformation of the graph of f(x) = |x| when it is changed to f(x) = |x - 3| + 2.

Back

The graph shifts 3 units to the right and 2 units up.

Front

What is the minimum value of the function y = |x - 4|?

Back

The minimum value is 0, occurring at x = 4.

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 is the effect of adding a constant to the absolute value function, such as in f(x) = |x| + c?

Back

Adding a constant c shifts the graph vertically by c units. If c is positive, the graph shifts up; if c is negative, it shifts down.

Front

What is the equation of the absolute value function that has a vertex at (2, -3)?

Back

The equation is f(x) = |x - 2| - 3.

Front

How do you determine the x-intercepts of the function f(x) = |x - 1| - 2?

Back

Set f(x) = 0 and solve for x: |x - 1| - 2 = 0, which gives x = 3 and x = -1.

Front

What is the general form of a piecewise function?

Back

A piecewise function is defined by different expressions based on the input value, typically written as: f(x) = { expression1 for condition1, expression2 for condition2, ... }.