Question

Evaluate the function as indicated determine its domain and range.

2x+1 , X<0
FX=
2x+2 ,X>or equal to 0

a. F(-1) b.f(0) c.F(2) d.F(t^2+1)

Answer 1

-1<0
so use 2x+1
2(-1)+1=-2+1=-1
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Answer 2

sorry use 2x+1 for what?

Answer 3

can you explain to me what its asking me to do

Answer 4

-1<0 so use 2x+1 to evaluate F at x=-1

Answer 5

F(-1) means "Evaluate F(x) when x=-1"

Since -1 is less than 0, this means that F(x) = 2x+1. This is because F(x) = 2x+1 when x < 0

Does that clear things up a bit?

Answer 6

oh so after i plugg in -1 i get fx=-1 is this my domain?

Answer 7

you plug x=-1 into F(x) = 2x+1 to get F(-1) = 2(-1)+1 = -2+1=-1

So F(-1) = -1

Answer 8

Your domain is the set of all allowable inputs. Since you can plug in any number, the domain is the set of all real numbers.

Answer 9

ooh i c so i do the same with b c d using whichever functions satisfy X>or equal to 0>?

Answer 10

yes, you got it

Answer 11

hold on lemme do another

Answer 12

so for instance, for part C, F(x) = 2x+2 because x >= 0 (since x=2 is greater than or equal to 0)

Answer 13

hmm do i have to plugg in a b and d too?

Answer 14

or is fx that satisfies f(x)=2x+2 enough?

Answer 15

1

Answer 16

are you referring to part b?

Answer 17

i mean why did you only use F(2)?

Answer 18

I was referring to part c)

Answer 19

oh i get it so each of those letters are like seperate problems

Answer 20

yes, that's right

Answer 21

thanks alot jim can you just tell me for like domain how you know you can plugg in all numbers and get all real numbers

Answer 22

If you combine x<0 and x>=0, you basically get that x can be any number. Another way to see this: x < 0 means "x is a negative number" and x>=0 means "x is nonnegative (ie zero or positive)"


So because this encapsulates every possible number (positive, negative, or zero), any number will work for x

Answer 23

ooh do u have a method for range aswell?

Answer 24

sorry for all the questions man u really amazing explain soo well

Answer 25

no that's good that you're asking a lot of questions

Answer 26

to find the range, you can either graph it and find the possible outputs (ie the y values)

Answer 27

or you can plug in the extremes in the domain. In other words, say x=0, then 2x+1=1 and 2x+2=2, so there's a gap from 1 to 2 in the range


This means that the range is \[y<1 \ \ \textrm{or} \ \ y\ge2\]

Answer 28

Here's a graph of the piecewise function (see attached)

Answer 29

thanks a million jim

Answer 30

looking at the graph, we can see that there is a gap where the y values cannot equal any number in the range from 1 to 2 (but it can equal 2 itself)

Answer 31

oh so 1 and 2 inclusive

Answer 32

No, those are the values that y CANNOT equal


So the range in interval notation is \[(-\infty,1)\cup[2,\infty)\]


Imagine the number line, but you "punched" out numbers in the range from 1 to 2

Answer 33

Im all set now thanks