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1 answer:
Answer: (A) vertical asymptote: x = 2, horizontal asymptote: y = 1
<u>Step-by-step explanation:</u>
<u>Vertical Asymptote</u> is the restriction on the x-value. The denominator cannot be zero, so x - 2 ≠ 0 ⇒ x ≠ 2
The restricted value on x is when x = 2 <em>which is the vertical asymptote</em>
<u>Horizontal Asymptote</u> (H.A.) is the restriction on the y-value. This is a comparison of the numerator (n) and denominator (m). There are 3 rules that will help you:
- n > m No H.A. (use long division to find slant asymptote)
- n = m H.A. is the coefficient of n divided by coefficient of m
- n < m H.A. is 0
In the given problem, n < m so y = 0, however there is also a vertical shift of up 1 so the H.A. also shifts up. This results in H.A. of y = 1
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Answer:
x = 1.24
Step-by-step explanation:
In order to get that x down from its current position of exponential, you need to take either the log or the natural log of both sides. The power rule tells us that we can then pull the exponent down in front. So let's take the natural log of both sides:
We can bring the x down in front to give us:
ln(83) = x ln(35)
The right side of this is "stuck" together by multiplication, so we can undo that multilication by division of the ln(35). That leaves us with just x on the right:
Do this on your calculator and find that x = 1.24