Piecewise, Absolute Value Functions, & Transformations

Front

What is the parent function of absolute value?

Back

The parent function of absolute value is f(x) = |x|.

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

How can you determine if a relation is a function?

Back

A relation is a function if each input has exactly one output. This can be checked using the vertical line test on its graph.

Front

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

Back

The vertex of the function is the point (h, k).

Front

What does the 'a' in the absolute value function f(x) = a|x - h| + k represent?

Back

The 'a' represents the vertical stretch or compression and the direction of the opening of the absolute value graph.

Front

What is the effect of changing 'h' in the function f(x) = |x - h|?

Back

Changing 'h' shifts the graph horizontally. If h is positive, the graph shifts to the right; if h is negative, it shifts to the left.

Front

What is the effect of changing 'k' in the function f(x) = |x| + k?

Back

Changing 'k' shifts the graph vertically. If k is positive, the graph shifts up; if k is negative, it shifts down.

Front

How do you find the value of a function at a specific point, such as f(-3)?

Back

To find f(-3), substitute -3 into the function's equation and simplify.

Front

What is the equation of the absolute value function that has been shifted up by 4 units?

Back

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

Front

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

Back

The range of f(x) = |x| is [0, ∞) because the output is always non-negative.