Absolute Value Functions Review

Front

What is the domain of the absolute value function?

Back

(-infinity, infinity)

Front

What is the general form of an absolute value function?

Back

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

Front

How does the graph of an absolute value function behave as x approaches infinity?

Back

The graph approaches infinity as x approaches infinity.

Front

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

Back

It reflects the graph across the x-axis.

Front

What is the vertex of the function f(x) = -|x - 2| - 7?

Back

The vertex is at the point (2, -7).

Front

How do you determine the distance represented by an absolute value expression?

Back

The absolute value expression |x| represents the distance from x to 0 on the number line.

Front

What transformations are applied to the function f(x) = |x| to obtain f(x) = -|x| + 2?

Back

Reflection across the x-axis and a vertical shift up by 2 units.

Front

What is the range of the function f(x) = -|x| + 2?

Back

The range is (-infinity, 2].

Front

How do you write an absolute value function that is shifted 3 units to the left and 4 units up?

Back

f(x) = |x + 3| + 4.

Front

What is the effect of a horizontal shift on the graph of an absolute value function?

Back

It moves the graph left or right along the x-axis.