Functions
A function is a relation that assigns to each number in the domain exactly one number in the range. The domain of a function is the set of possible inputs that the function may assign to and produce meaningful outputs. The range is the set of possible outputs.
In Lab 7, we used Excel formulas to produce a sequence frequencies of musical notes. The Excel formula we used is an example of function. Indeed, a function is frequently described by a formula (equality, to be a more accurate). Another way to describe a function is to use a graph.
A linear function is determined by its slope m and the y-intercept b. If f is a linear function with the slope and the y-intercept b, then for any number x in the domain of f, there is an output, f(x), given by f(x) = mx + b. One reason that the function defined by f(x) = mx + b is called a linear function is that its graph is a line.
Example: Create a graph for the linear function f(x) = 2x − 1 over the domain − 5 ≤ x ≤ 5.
Solution: We start with creating a table which consists of a column for x and another column for f(x) = 2x − 1.
Input x in the cell
A1 and f(x) = 2x − 1 in
the cell B1.
Input -5, -4, -3 in the cells A2, A2
and A3 respectively and the use autofill to generate
numbers -2, -1, … 5.
Input =2*A2-1 in the cell B2 and use
autofill to generate the outputs for f.
To create the graph, we use the scatter plot function of Excel.
Highlight the cells A1:B12. Then click
Insert and look for “Insert Scatter”.
Click Scatter to create a scatter plot
Select the chart, click + to add the trendline.
Create a table consists of integer inputs and a graph for the function f(x) = 3x − 2 over the domain − 5 ≤ x ≤ 5.