SOLUTION: Please help me with this problem. Thank You! Graph the function. f(x)= 4x+2, if x<-2 x , if -2(less than or equal to sign) x (less than or equal to sign) 3 3x

Algebra ->  Rational-functions -> SOLUTION: Please help me with this problem. Thank You! Graph the function. f(x)= 4x+2, if x<-2 x , if -2(less than or equal to sign) x (less than or equal to sign) 3 3x      Log On


   

Question 134359: Please help me with this problem. Thank You!
Graph the function.
f(x)= 4x+2, if x<-2
x , if -2(less than or equal to sign) x (less than or equal to sign) 3
3x-1, if x>3
everything after the equals sign are in one bracket ({)
Please help me-I keep getting this wrong on my assignments and tests. Thank You!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: for some reason, some of the following images do not display correctly in Internet Explorer. So I recommend the use of Firefox to see these images.



Let's break up this piecewise function into 3 pieces

Piece # 1:
y=4x%2B2


Let's graph y=4x%2B2 (tell me if you need help with graphing)

graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C4x%2B2%29


Now let's only draw the part of the graph that is less than x=-2. In other words, erase everything to the right of x=-2 for the graph y=4x%2B2


Graph of y=4x%2B2 with the condition that x%3C-2





Piece # 2:


Now let's graph y=x



graph%28500%2C500%2C-10%2C10%2C-10%2C10%2Cx%29


Now since we have the condition -2%3C=x%3C=3, this means that our new graph should look like:

Graph of y=x from x=-2 to x=3




Piece #3


Now let's graph y=3x-1



graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C3x-1%29



Now because the corresponding inequality is x%3E3, this means that we only draw the part of the graph that is greater than 3


So the graph should look like


Graph of y=3x-1 from x=3 to infinity



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Now let's combine the three graphs and plot them on the same coordinate system


Graph of