Absolute Value Functions

Front

What is the definition of an absolute value function?

Back

An absolute value function is a function that returns the non-negative value of a number, defined as f(x) = |x|, where |x| is the distance of x from 0 on the number line.

Front

What is the vertex of the parent absolute value function y = |x|?

Back

The vertex of the parent absolute value function y = |x| is at the point (0, 0).

Front

How does the graph of y = |x - 4| differ from y = |x|?

Back

The graph of y = |x - 4| is the graph of y = |x| shifted 4 units to the right.

Front

What transformation does y = |x + 2| represent compared to y = |x|?

Back

The graph of y = |x + 2| is the graph of y = |x| shifted 2 units to the left.

Front

What is the effect of the negative sign in front of the absolute value in y = -|x|?

Back

The negative sign reflects the graph of the absolute value function across the x-axis.

Front

What does the equation y = |x| + 3 represent in terms of transformation?

Back

The equation y = |x| + 3 represents the graph of y = |x| shifted 3 units upward.

Front

How do you find the vertex of the function f(x) = |2x - 6| + 4?

Back

To find the vertex, set the inside of the absolute value to zero: 2x - 6 = 0, which gives x = 3. Then, substitute x = 3 into the function to find f(3) = |0| + 4 = 4. The vertex is (3, 4).

Front

What transformation does y = |x| - 5 represent?

Back

The graph of y = |x| - 5 is the graph of y = |x| shifted 5 units downward.

Front

What is the general form of an absolute value function?

Back

The general form of an absolute value function is f(x) = a|bx - h| + k, where (h, k) is the vertex.

Front

What does the parameter 'a' in the function f(x) = a|x| do?

Back

The parameter 'a' affects the vertical stretch or compression of the graph. If |a| > 1, the graph is stretched; if 0 < |a| < 1, it is compressed.