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1) Let f(x) = {x²  for x < 1

                    {2x - 5  for x ≥ 1

 

(a) Graph the piecewise-function from x = -2 to x = 4.

 

(b) Find the domain for all f(x).

 

(c) Find the range for all f(x).

 

(d) Is f(x) continuous on its domain? Yes or No

 Nov 23, 2019
edited by GAMEMASTERX40  Nov 23, 2019
edited by GAMEMASTERX40  Nov 23, 2019
edited by GAMEMASTERX40  Nov 23, 2019
 #1
avatar+105476 
+2

(a)  Here's the graph : https://www.desmos.com/calculator/6ur4exjxcr

 

(b) The domain fo the first function  is  (-inf, 1)

 

The domain for the second function  is  [ 1, inf )

 

(c)  The range of the first function   is [ 0 , inf )

 

The range of the second function is  [ -3, inf )

 

(d) Not contunious....as the graph shows

 

cool cool cool 

 Nov 23, 2019
 #2
avatar+49 
+1

Hey CPhill I found a mistake with your graph which threw me off so I fixed it here: https://www.desmos.com/calculator/tqvci9lcnt

As you can see you are graphing the function from x = -2 to x = 4 and your graph had the signs facing the wrong way. Maybe you can look it over and fix (b), (c), and (d) in the problem which I think affects it from the mistake.

GAMEMASTERX40  Nov 23, 2019
edited by GAMEMASTERX40  Nov 23, 2019
edited by GAMEMASTERX40  Nov 23, 2019
 #3
avatar+105476 
+1

Fixed....it doesn't affect anything

 

If   x^2   existed  at x  = 1    then  y  = 1

 

At x = 1  then the yvalue for 2x - 5  =  -3

 

So...as the graph shows  here : https://www.desmos.com/calculator/vydmkdw06y, it is not continuous...

 

 

 

cool cool cool

CPhill  Nov 23, 2019

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