Graph Vocab and Graphs of Functions

General Graph Vocab

General Graph Vocab

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.

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.

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.

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.

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.

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.

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

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.

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.

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 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.

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.

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.