Functions of the Form <em>y = x</em>
Functions of the form \(y=x\)
Functions of the form \(y=mx+c\) are called straight line functions. In the equation, \(y=mx+c\), \(m\) and \(c\) are constants and have different effects on the graph of the function.
Example
Question
Complete the following table for \(f(x)=x\) and plot the points on a set of axes.
|
\(x\) |
\(-\text{2}\) |
\(-\text{1}\) |
\(\text{0}\) |
\(\text{1}\) |
\(\text{2}\) |
|
\(f(x)\) |
\(-\text{2}\) |
-
Join the points with a straight line.
-
Determine the domain and range.
-
About which line is \(f\) symmetrical?
-
Using the graph, determine the value of \(x\) for which \(f(x)=4\). Confirm your answer graphically.
-
Where does the graph cut the axes?
Substitute values into the equation
|
\(x\) |
\(-\text{2}\) |
\(-\text{1}\) |
\(\text{0}\) |
\(\text{1}\) |
\(\text{2}\) |
|
\(f(x)\) |
\(-\text{2}\) |
\(-\text{1}\) |
\(\text{0}\) |
\(\text{1}\) |
\(\text{2}\) |
Plot the points and join with a straight line curve
From the table, we get the following points and the graph:
\((-2;-2), (-1;-1), (0;0), (1;1), (2;2)\)
Determine the domain and range
Domain: \(x\in \mathbb{R}\)
Range: \(f(x)\in \mathbb{R}\)
Determine the value of \(x\) for which \(f(x)=4\)
From the graph we see that when \(f(x)=4\), \(x=4\). This gives the point \((4;4)\).
Determine the intercept
The function \(f\) intercepts the axes at the origin \((0;0)\).
This lesson is part of:
Functions I