Answer:
A. f(x): [tex](0,\frac{-1}{3})[/tex], g(x): (0,0)
B. f(x): 'y= 0' as horizontal asymptote, g(x): 'x= 4' as vertical asymptote.
Step-by-step explanation:
We are given the functions, [tex]f(x)=\frac{1}{x-3}[/tex] and graph of g(x).
Part A: We know that,
'Y-intercepts are the points where the graph of the function crosses y-axis'.
That is, 'y-intercept is obtained when x= 0'.
So, we have,
When x= 0, [tex]f(0)=\frac{1}{0-3}[/tex] i.e. [tex]f(0)=\frac{-1}{3}[/tex].
Thus, the y-intercept of function f(x) is the point [tex](0,\frac{-1}{3})[/tex].
Also, from the graph of g(x), we see that, the graph crosses y-axis at the point (0,0).
Thus, the y-intercept of g(x) is (0,0).
Part B: We know that,
'Asymptotes are the line or curves approaching the graphs of the functions arbitrarily close'.
Now, as we have the function f(x) is a rational function and the degree of numerator is less than the degree of the denominator.
So, the function f(x) will have 'y= 0' as the horizontal asymptote.
Also, from the graph of the function g(x), we see that,
The line 'x= 4' is the vertical asymptote as it is approaching the graph closely.
So, the function g(x) have 'x= 4' as the vertical asymptote.
