Patterns and Linear Functions
Standard
F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features...Also A.CED.2
Goals for this section:
To identify and represent patterns that describe linear functions.
Independent Variables
- Inputs
- On the horizontal x-axis (your x-value)
- The value of the independent variable is whatever you choose to input into the function.
Dependent Variables
- Outputs
- On the vertical y-axis (your y-value)
- The value of the dependent variable depends on what x-value is used in the function.
Function:
To describe a function, we can see it as a relationship that pairs each input value with its output value. An input value is taking any x-value and plugging it into the function to provide a y-value.
- A function has EXACTLY one output for every input. If you get two outputs then it is not a function!
Linear Function:
We can relate what a linear function looks like by using y=mx+b.
- y is the dependent variable
- x is the independent variable
- m is the slope, a constant
- b is the y-intercept, a constant
It is of the first degree, meaning, the x variable's "degree" is 1. The degree is the exponent that you see with the independent variable, usually x. If there is no exponent it is implied to be 1.
This means that the line will be non vertical or a diagonal line.
We have a function like y=2x+3 where the y-intercept is 3 and the slope of the line is 2. Notice how the line is not a straight but diagonal because we have an input of any x that gives us an output value of a y.
External Resources
This video will explain what it means for something to be a function.