Lesson 2 3 Piecewise and Absolute Value Functions

Lesson 2 -3: Piecewise and Absolute Value Functions Advanced Math Topics

n Piecewise functions n A function defined by two or more equations n n Domain n n Each equation applies to a different part of the domain it is usually described in the problem and can just be rewritten for the answer Range n found by taking the endpoints (if there any) for the domain intervals and plugging them into the appropriate function to find the y-values

Summary n f(x)= different things for different sections of the graph n Remember what open dots and closed dots mean? ?

Piece Wise Functions Step 1 Graph the linear function f(x) = – 1 for x ≤ 3. Since 3 satisfies this inequality, begin with a closed circle at (3, 2).

Step 2 Graph the constant function f(x) = – 1 for x > 3. Since x does not satisfy this inequality, begin with an open circle at (3, – 1) and draw a horizontal ray to the right.

Answer: The function is defined for all values of x, so the domain is all real numbers. The values that are y-coordinates of points on the graph are all real numbers less than or equal to 2, so the range is {y | y ≤ 2}.

A. B. C. D.

n Absolute Value Function n A function with a variable inside the absolute value bars n The graph makes a “V” shape

To Graph Take everything inside the | | and set it equal to 0. The x-value you get is the x-value for the corner. n Plug the x-value in and solve for y n The resulting ordered pair is where you absolute value graph starts! (the corner) n Plug in two x-values on either side of the corner to find ordered pairs to finish the graph n

To Find Domain and Range Domain: ARN there are no restrictions on the x -values you can plug into an absolute value graph n Range: determined from the y-values, y will be > or < the y-value of the corner n

Summary

Absolute Value

Graphs

n. Graph f(x) = |x| – 2 and g(x) = |x| + 3 on the same coordinate plane. Which answer choice is not true about the pair of graphs?

Identify the type of function