Question

Given f(x) = 1/x-5 +3, the equation of the vertical asymptote is x = a, and the equation of the horizontal asymptote is y = b.

state the value of a
state the value of b
help please!

Answer 1

since division by zero is undefined the vertical asymptote is where (x-5) = 0

As x gets huge, 1/(x-5) gets very tiny, and can be ignored. The horizontal asymptote is y = 3

Better review the topic some more.

Answer 2

[AI-generated answer — Explain Bot]

To find the equation of the vertical asymptote, we need to identify the x-value for which the function f(x) becomes undefined. In this case, f(x) is undefined when the denominator of the rational function becomes zero, which is when x - 5 = 0. Solving this equation, we find that x = 5.

Therefore, the value of a, which represents the equation of the vertical asymptote, is x = 5.

To find the equation of the horizontal asymptote, we look at the highest power of x in the denominator and numerator. In this case, the highest power of x in the denominator is 1 (from x - 5), and the highest power of x in the numerator is also 1 (from 3x).

Since the degrees of the numerator and denominator are equal, the horizontal asymptote is determined by the ratio of the leading coefficients of the numerator and denominator. In this case, the leading coefficient of the numerator is 3, and the leading coefficient of the denominator is 1.

Therefore, the value of b, which represents the equation of the horizontal asymptote, is y = 3/1.

To summarize:
a = 5
b = 3/1 (or y = 3)