The asymptotes of the function is y = ₋2 and its y intercept form is (0,1)
What are asymptotes and y-intercept form?
Asymptotes are curves that approach a line but never actually touch it. An asymptote is a line at which the graph of a function converges, in other words.
Asymptotes come in two different varieties.
The horizontal asymptote (HA) has the equation y = k since it is a horizontal line.
Since it is a vertical line, the vertical asymptote's equation has the form x = k.
The graph's intersection with the y-axis is known as the y-intercept. Finding the intercepts for any function with the formula y = f(x) is crucial when graphing the function. A function's intercept is the location on the axis where the function's graph crosses it.
Given f(x) = 3/x ₊ 1 ₋ 2
x₋1 = 0
x = 1
Consider the rational function R(x) = axⁿ/bx^m
where n is the degree of numerator and m is the degree of denominator.
- if n<m, then the x axis, y = 0, is the horizontal asymptote.
- if n = m, then the horizontal asymptote is the line y = a/b
- if n>m, then there is no horizontal asymptote.
Here we have n = 1 and m = 1.
Since n = m, the horizontal asymptote is the line y = a/b
where a = ₋2 and b = 1.
therefore y = ₋2
the slope intercept form is : y=mx ₊ b
y = 3/x₊1 ₋2
therefore y = (0,1)
Hence we get the asymptote as y = -2 and y intercept form as (0,1)
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