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

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

Summary f(x)= different things for different sections of the graph 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 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.

Absolute Value Function A function with a variable inside the absolute value bars 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. Plug the x-value in and solve for y The resulting ordered pair is where you absolute value graph starts! (the corner) Plug in two x-values on either side of the corner to find ordered pairs to finish the graph

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

Summary

Absolute Value

Graphs

Graph f(x) = |x| – 2 and g(x) = |x| + 3 on the same coordinate plane 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

Identify the type of function

Identify the type of function