Graphing Absolute Value of Functions

Front

What is the range of the absolute value function?

Back

[0, infinity)

Front

What transformations occur in the function f(x) = |x - 5| - 2?

Back

Down 2, right 5

Front

What is the standard equation of the absolute value function?

Back

f(x) = |x| + 4

Front

How does the absolute value parent function transform when it is stretched more narrowly?

Back

It becomes steeper and shifts right.

Front

What does the equation y = |x - 3| indicate about the graph's movement?

Back

The graph slides right 3.

Front

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

Back

(0, 0)

Front

How does the absolute value function behave for negative inputs?

Back

It reflects the negative inputs to positive values.

Front

What is the effect of adding a constant outside the absolute value function?

Back

It shifts the graph vertically.

Front

What is the effect of subtracting a constant inside the absolute value function?

Back

It shifts the graph horizontally.

Front

What is the general form of an absolute value function?

Back

f(x) = a|bx - h| + k, where (h, k) is the vertex.