Graph of piecewise functions, Algebra

We should graph a couple of these to make sure that we can graph them as well.

Example: Sketch the graph of the following piecewise function.

899_Graph of piecewise functions.png

Solution

Now while we are graphing piecewise functions we are in fact graphing various functions at once, except we are just going to graph them on very particular intervals.  In this case we will be graphing the given two functions,

- x2 + 4           on x < 1

2 x -1  on x ≥ 1

We'll have to be a little careful with what is going on right at x =1 as technically that will only be valid for the bottom function. But, we'll deal along with that at the very end while we actually do the graph.  For now, we will employ x = 1 in both functions.

Here the first thing to do is to get a table of values for each function on the particular range and again we will employ function. x = 1 in both even though technically it only have to be used with the bottom

x

- x2 + 4

( x, y )

-2

0

(-2, 0)

-1

3

( -1, 3)

0

4

(0, 4)

1

3

(1, 3)

 

x

 

2 x -1

 

( x, y )

1

1

(1,1)

2

3

( 2, 3)

3

5

(3, 5)

Following is a sketch of the graph and notice how we indicated the points at x = 1 .  For the top function we utilized an open dot for the point at x = 1 and for the bottom function we utilized a closed dot at x = 1 .  In this way we make it apparent on the graph that only the bottom function actually has a point at x = 1 .

614_Graph of piecewise functions1.png

Notice that as the two graphs didn't meet at x = 1 we left a blank space in the graph. Do not connect these two points along a line. There actually does have to be a break there to indicate that the two portions do not meet at x = 1 .

Sometimes the two portions will meet at these points & at other times they won't.  We have not ever expected them to meet or not to meet till we've in fact sketched the graph.

Posted Date: 4/8/2013 1:14:41 AM | Location : United States







Related Discussions:- Graph of piecewise functions, Assignment Help, Ask Question on Graph of piecewise functions, Get Answer, Expert's Help, Graph of piecewise functions Discussions

Write discussion on Graph of piecewise functions
Your posts are moderated
Related Questions
To estimate the size of the bear population in Keweenaw Pennisula, conservationists captured, tagged and released 50 bears. One year later, a random sample of 100 bears included on


write the expression in exponential form 6^sqrt9^3

of the 400 doctors attending a conference 240 practice family medicine and 130 were from countries outside the US.1/3 of the family medicine practitioners were not from the US. Wha

Find out the symmetry of equations.                                                  y = x 2 - 6x 4 + 2 Solution First we'll check for symmetry around the x-axis. It

Solve x =√(x+ 6) . Solution In this equation the fundamental problem is the square root.  If it weren't there we could do the problem.  The whole procedure that we're going

what is the missing angle of 37 degree and 92 drgees

Factor Theorem For the polynomial P ( x ) , 1. If value of r is a zero of P ( x ) then x - r will be a factor of P ( x ) . 2. If x - r is a factor of P ( x ) then r will

(y+1/3x)^2

Thirty percent of the students in a mathematics class received an “A.” If 18 students received an “A,” which of the following represents the number of students in the class?