Let
Find the range of 
. Give your answer as an interval.
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+23254 When graphed, this is a hyperbola. The question is: What y-value is impossible?
If you find the lim(x→∞) [3x - 7] / [x + 1], you will be able to answer the question.
Rewrite [3x - 7] / [x + 1] = [3 - 7/x] / [1 + 1/x] (by dividing all terms by x0
---> lim(x→∞) [3 - 7/x] / [1 + 1/x] = 3.
To show that 3 is impossible, try to solve the equation: 3 = (3x - 7) / (x + 1)
Multiply both sides by x + 1 ---> 3(x + 1) = 3x - 7 ---> 3x + 3 = 3x - 7
---> 3 = -7 Impossible!
Thus, the range is all numbers but 3.
+23254 When graphed, this is a hyperbola. The question is: What y-value is impossible?
If you find the lim(x→∞) [3x - 7] / [x + 1], you will be able to answer the question.
Rewrite [3x - 7] / [x + 1] = [3 - 7/x] / [1 + 1/x] (by dividing all terms by x0
---> lim(x→∞) [3 - 7/x] / [1 + 1/x] = 3.
To show that 3 is impossible, try to solve the equation: 3 = (3x - 7) / (x + 1)
Multiply both sides by x + 1 ---> 3(x + 1) = 3x - 7 ---> 3x + 3 = 3x - 7
---> 3 = -7 Impossible!
Thus, the range is all numbers but 3.
