1. Graph Vocab and Graphs of Functions

2. General Graph Vocab

3. General Graph Vocab

4. Parts of a graph…
Increase – A function is “increasing” when the y-value increases as the x-value increases.
Decrease – A function is “decreasing” when the y-value decreases 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.

5. Parts of a graph…
Linear: Part of a function is linear when it makes a straight line.
***Each part of this graph is linear because each section is a straight line. However the entire graph is non-linear because the entire graph is not one big 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.

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

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

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

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

10. Remember:
A function is a rule that relates two quantities so that each input value corresponds to exactly one output value.

11. Graphs of Functions
In order for a graph to be a function, each x can only have ONE y.
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.

12. In order for a graph to be a function, each x can only have ONE y.
This graph is not a function because of the points (1,40) and (1,50), (2,75) and (2,65) etc.
Is this graph a function? Why or why not?
Yes, each x input has only one y output.

13. 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.

14. Determine if the relationship represents a function
Determine if the relationship represents a function. Does it pass the vertical line test?
No, this fails the VLT
The vertical line touches the graph in two places meaning the x input of 1.5 has two different outputs.
The relationship is not a function.

15. The vertical line touches the graph in only one place at a time
Determine if the relationship represents a function. Does it pass the vertical line test?
Yes, this passes the VLT x y
The vertical line touches the graph in only one place at a time
The relationship is a function.

16. Determine if the relationship represents a function
Determine if the relationship represents a function. Does it pass the vertical line test?
Yes, this passes the VLT
The relationship is a function.