Graphs of Functions Graphs of Functions

43210 In addition to level 3.0 and beyond what was taught in class, the student may: Make connection with other concepts in math. Make connection with other content areas. The student will understand and explain the difference between functions and non-functions using graphs, equations, and tables. Compare properties of a function to a non- function. The student will be able to model and evaluate functions and non-functions. Use graphs, equations, and tables to determine functions and non- functions. With help from the teacher, the student has partial success with level 2 and 3 elements. Even with help, students have no success with the functions. Focus 6 - Learning Goal #1: Students will understand and explain the difference between functions and non-functions using graphs, equations, and tables.

A function is a rule that relates two quantities so that each input value corresponds to exactly one output value. Define-

In order for a graph to be a function, each x can only have ONE y. Give an example of why this graph is not a function. Is this graph a function? Why or why not? Yes, each x input has only one y output.

Is this graph a function? Why or why not? NO, each x input has more than one y output. Is this graph a function? Why or why not? Yes, each x input has only one y output.

Vertical Line Test When looking at a graph, you can tell if a drawing is a function if it passes the vertical line test. This means you can draw a vertical line and it will only touch the drawing (graphed figure) one time. If it touches the drawing (graphed figure) more than once, it is not a function.

Determine if the relationship represents a function. Does it pass the vertical line test? The relationship is not a function.

Determine if the relationship represents a function. Does it pass the vertical line test? The relationship is a function. x y

Determine if the relationship represents a function. Does it pass the vertical line test? The relationship is a function.

Parts of a graph… Increase – A function is “increasing” when the y-value increases as the x-value increases. Interval – A section of the graph. ◦This function is increasing for the interval shown. It may be increasing or decreasing elsewhere. Decrease – A function is “decreasing” when the y-value decreases as the x-value increases.

Parts of a graph… Linear: A function is linear when it makes a straight line. *Each part of this graph is linear because each section is a straight line. Non-Linear: A function is non-linear when it is curved. *Each part of this graph is non-linear because each section is curved.

At what intervals is this function increasing? Intervals are written in between brackets [ ]. 1.[0.5, 1] This means it is increasing from 0.5 to 1 along the x- axis. 2.[2, 3] This means it is increasing from 2 to 3 along the x-axis.

At what intervals is this function decreasing? 1.[-1, 0.5] This means it is decreasing from -1 to 0.5 along the x- axis. 2.[1, 2] This means it is decreasing from 1 to 2 along the x- axis.

At what intervals is this function linear? 1.[-1, 0] This means it is linear from -1 to 0 along the x-axis. 2.[1, 2] This means it is linear from 1 to 2 along the x-axis.

At what intervals is this function non- linear? 1.[0, 1] This means it is non-linear from 0 to 1 along the x-axis. 2.[2, 3] This means it is decreasing from 2 to 3 along the x- axis.