Question

How do you graph the function $f\left( x \right)=2x$ ?

Answer 1

Problems of this type can be easily solved by converting the function into a simple coordinate geometrical equation first, as $y=2x$ . After that we select two $x$ values, and plug them into the equation to find the corresponding $y$ values. Now, we plot the two points on graph paper and connect them using a line, which will be the graph of the given function.

Complete step by step answer:
The given function we have is
$f\left( x \right)=2x$
We rewrite this function in the form of an equation,
$\Rightarrow y=2x$
As, this is an equation of a straight line and we know that any line can be graphed connecting two points. We have to select two $x$ values, and plug them into the equation to find the corresponding $y$ values.
We now choose $0$ to substitute in for in for $x$ to find the ordered pair. Replacing the variable $x$ with $0$ in the expression, we get
$\Rightarrow f\left( 0 \right)=2\cdot 0$
$\Rightarrow f\left( 0 \right)=0$
$\Rightarrow y=0$
Hence, for $x=0$ we get $0$ as the $y$ value.
Again, we replace the variable $x$ with $5$ in the expression, as
$\Rightarrow f\left( 5 \right)=2\cdot 5$
$\Rightarrow f\left( 5 \right)=10$
$\Rightarrow y=10$
Hence, for $x=5$ we get $10$ as the $y$ value.
We get the coordinates of the two points $\left( 0,0 \right)$ and $\left( 5,10 \right)$
Now, connecting the two points we get the graph of the line, $y=2x$
Therefore, we graph the line by connecting the points $\left( 0,0 \right)$ and $\left( 5,10 \right)$ .

Note:
Instead of connecting two points to get the line we can also graph the function by comparing the equation with the general straight-line equation, $y=mx+c$ . Hence, the slope we get is $2$ and the $y$ intercept is $0$ . As the line has zero $y$ intercept using a protractor at the origin to draw the angle of the corresponding slope, we will be able to plot the function $f\left( x \right)=2x$ on graph paper.