Discovering the Characteristics of Linear Functions
Discovering the Characteristics
The standard form of a straight line graph is the equation \(y=mx+c\).
Domain and range:
The domain is \(\{x:x\in \mathbb{R}\}\) because there is no value of \(x\) for which \(f(x)\) is undefined.
The range of \(f(x)=mx+c\) is also \(\{f(x):f(x)\in \mathbb{R}\}\) because \(f(x)\) can take on any real value.
Intercepts:
The \(y\)-intercept:
Every point on the \(y\)-axis has an \(x\)-coordinate of \(\text{0}\). Therefore to calculate the \(y\)-intercept, let \(x=0\).
For example, the \(y\)-intercept of \(g(x)=x-1\) is given by setting \(x=0\):
\begin{align*} g(x)& = x-1 \\ g(0)& = 0-1 \\ & = -1 \end{align*}This gives the point \((0;-1)\).
The \(x\)-intercept:
Every point on the \(x\)-axis has a \(y\)-coordinate of \(\text{0}\). Therefore to calculate the \(x\)-intercept, let \(y=0\).
For example, the \(x\)-intercept of \(g(x)=x-1\) is given by setting \(y=0\):
\begin{align*} g(x)& = x-1 \\ 0& = x-1 \\ \therefore x& = 1 \end{align*}This gives the point \((1;0)\).
This lesson is part of:
Functions I