I have to find out if there equivalent? 96 miles on 4 gallons,380 miles on 15 gallons?
2 answers:
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Answer as an inequality:
Answer in interval notation:
Answer in words: Set of positive real numbers
All three represent the same idea, but in different forms.
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Explanation:
Any log is the inverse of an exponential equation. Consider a general base b such that f(x) = b^x. The inverse of this is
For the exponential b^x, we cannot have b^x = 0. We can get closer to it, but we can't actually get there. The horizontal asymptote is y = 0.
Because of this, has a vertical asymptote x = 0 (recall that x and y swap, so the asymptotes swap as well). This means we can get closer and closer to x = 0 from the positive side, but never reach x = 0 itself.
The domain of is x > 0 which in interval notation would be
. This is the interval from 0 to infinity, excluding both endpoints.
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The natural log function Ln(x) is a special type of log function where the base is b = e = 2.718 approximately.
So,
allowing all of what was discussed in the previous section to apply to this Ln(x) function as well.
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In short, the domain is the set of positive real numbers. We can't have x be 0 or negative.
y = 2x - 3
for x = 0 → y = 2(0) - 3 = -3 → (0, -3)
for x = 2 → y = 2(2) - 3 = 1 → (2, 1)
y = -2x + 5
for x = 0 → y = -2(0) + 5 = 5 → (0, 5)
for x = 2 → y = -2(2) + 5 = 1 → (2, 1)
Answer: A. (2, 1)
