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How To Sketch The Graph of a Piecewise Function

A piecewise function is a function that is defined differently on different part of its domain. One of the most common function is the absolute value function. Absolute value function is defined as

$|x|=\begin{cases}x&\text{ if } x\geq 0<img src=$ -x&\text{ if } x>0\end{cases}" border=0 align=absmiddle>

This definition tells us that if your $x$ is non-negative ( $x\geq 0$ ) use the rule $f(x)=x$ , otherwise use the rule $f(x)=-x$ .

In the video playslist below you will learn how to graph a piece wise function. You will also learn that given a graph of a piece wise function, how to construct the definition of the function itself and finally there is some tutorial how to graph a piecewise function on your calculator.

How To Find Equation of Line by Using The Slope Intercept Form

If a line has slope $m$ and intercept $b$ then the equation of this line is $y=mx+b$ . This formula is an implication of the point-slope formula. The intercept $b$ tells us that the lline passes through the point $(0,b)$ . Then by using the point-slope the equation of the line is $y-b=m(x-0)$ that simplifies to $y=mx+b$ . One advantage of the slope-intercept form is that we can easily graph the line if the equation in the slope-intercept is given. For example we have an equation of a line $y=3x+4$ . We can read from the coefficient of $x$ that the slope is $3$ and also we can read from the constant term that the intercept is $4$ . Now to draw the graph of this line we just need to mark the point $(0,4)$ and then draw a straight line with slope 3.

The videos below will give you an example of how to find an equation in the slope-intercept form and also will teach you how to use this information to draw the graph of the line

How To Find The Equation of Line in The Point Slope Form

Recall that to compute the slope of the line we just need to find two points on the line. If $(x_1,y_1)$ and $(x_2,y_2)$ are on the line then the slope of the line is given by $\frac{x_2-x_1}{y_2-y_1}$ . Now if we want to find the equation of the line wher the slope of the line is given and passes through $(x_0,y_0)$ we can use the slope formula above to find the equation. If $(x,y)$ is any point on the line, then together with $(x_0,y_0)$ we can compute the slope, but here the slope is given say equals $m$ . Then we have

$\frac{y-y_0}{x-x_0}=m$

or $y-y_0=m(x-x_0)$

which we usually refer as the point-slope form of the equation of line.

The videos below will give you examples how to use this formula to find the equation of line