4.6.2 – Graphing Absolute Value Functions

• Recall, a function f(x) = |x| is consider an absolute value function

• What shape are the graphs for absolute value functions?

• All are in the shape of a “v”

• Some properties will determineif the graph opens up, or down,and if it is wide or narrow

Up or Down?

• For an absolute value function f(x) = a|x|, the a value will tell us if it opens up, or down

• If a > 0, then the graph opens up

• If a < 0, then the graph opens down

Narrow or Wide?

• The a value in f(x) = a|x| also helps us determine if the graph is narrow, or wide, compared to f(x) = |x|

• If |a| > 1, then the graph is narrower than y = |x|

• If |a| < 1, then the graph is wider than y = |x|

How to graph?

• To graph the absolute value function f(x) = |x|, we will choose a positive x value to substitute

• From yesterday, what is one key property of the graphs of absolute value functions?

• Use the point of symmetry for a second point

• Example. Graph the function f(x) = 2|x|.• Up or down?

• Example. Graph the function f(x) = -3|x|.• Up or down?

• Example. Graph the function f(x) = -4|x|.• Up or down?

Using your Calculators

• Take out your graphing calculators• We will take a look at the a value and compare

when we start to change it

• Assignment• Pg. 208• 21-29 odd, 37-43 odd, 59