Analyze Absolute Value Graphs and Transformations

Front

What is the parent function of an Absolute Value?

Back

f(x) = |x|

Front

How does the graph of f(x) = |x - h| + k transform the parent function?

Back

It shifts the graph horizontally by h units and vertically by k units.

Front

What effect does a negative sign in front of the absolute value function have on the graph?

Back

It reflects the graph across the x-axis.

Front

What is the vertex of the function f(x) = |x - 3| + 4?

Back

The vertex is at the point (3, 4).

Front

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

Back

The range is [0, ∞).

Front

How do you determine the maximum value of a transformed absolute value function?

Back

The maximum value occurs at the vertex if the graph opens downwards.

Front

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

Back

The 'k' value represents a vertical shift of the graph.

Front

What is the effect of multiplying the absolute value function by a factor greater than 1?

Back

It vertically stretches the graph.

Front

What is the effect of multiplying the absolute value function by a factor between 0 and 1?

Back

It vertically compresses the graph.

Front

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

Back

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