2-5 Absolute Value Functions and Graphs

Vertex Maximum or minimum of the graph For the equation, the vertex is at

Identify the vertex for each function 1. f(x) = | 2x – 5 | 2. f(x) = | 3x + 6 | 3. f(x) = - |x + 1 | - 2

Graphing absolute value functions by making a table Find the vertex Make a table of values (at least 5!) Graph the function.

Find several ordered pairs for each function. Graph and on the same coordinate plane. Determine the similarities and differences in the two graphs. Find several ordered pairs for each function. x | x – 3 | 3 1 2 4 5 x | x + 2 | –4 2 –3 1 –2 –1 3 Example 6-3a

Graph the points and connect them. Answer: The domain of both graphs is all real numbers. The range of both graphs is The graphs have the same shape, but different x-intercepts. The graph of g (x) is the graph of f (x) translated left 5 units. Example 6-3b

Graph y = | x – 3 | + 3 X Y

Graph y = | 2x + 1 | X Y

X Y The recommended dietary allowance for vitamin C is 2 micrograms per day. Write an absolute value function for the difference Between the number of micrograms of Vit C you ate today x and the recommended amount. X Y

Graph X Y

Graph y = | -x – 5 | X Y

Graph y = | -3x | X Y