Question 60769This question is from textbook alegbra concepts and applications
: Find the domain of y = x+ 3 if the range is (-1,1,3,5)
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This question is from textbook alegbra concepts and applications
Answer by mszlmb(115)   (Show Source):
You can put this solution on YOUR website! Just as domain are the x values, range are the y values. To null out any confusion, "y" is the same as "f(x)" if that is the notation you are using.
For each range value -1, 1, 3, and 5, we will have an x value. To find the corresponding x to each y value, we just plug in the range for y, one at a time
-1:
y=x+3 replace y with -1
-1=x+3 minus three on both sides
-4=x there, so for the range value -1, the domain is -4.
1:
1=x+3 minus three
-2=x .: [the sign for 'therefore'] for the range 1, the domain is -2.
3:
3=x+3 minus three both sides
0=x so for range 3 domain is 0.
5:
5=x+3 minus three both sides
2=x so for range 5 domain is 2
We just put them in order. We were given range {-1,1,3,5} so our domain should be {X when y=-1, X when y=1, X when y=3, X when y=5} in that order. X when y=-1 was -4, X when y=1 was -2, X when y was 3 was 1, X when y was 5 was 2. Our answer is thus {-4,-2,1,2}.
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