Question

In Lesson 3.05 we discussed comparing the key features of two functions given in different forms. Given the functions below:

Answer 1

Answer:

A) f(x) has y-intercept at and g(x) has y-intercept at (0,0)

B) f(x) has asymptote as x= 0 and g(x) has asymptote as x= 4.

Step-by-step explanation:

The functions given are $f(x)=\frac{1}{x-3}$ and the graph of g(x).

A): Since, 'y-intercepts are the points where the graph of the function cuts y-axis'

So, 'at x=0, we obtain y-intercepts'.

Thus,

$f(0)=\frac{1}{0-3}$ implies $f(0)=\frac{-1}{3}$

Hence, $(0,\frac{-1}{3})$ is the y-intercept of f(x).

Now, we see that,  

The graph of the function g(x) crosses y-axis at the point (0,0).

Hence, the (0,0) is the y-intercept of the function g(x).

B): As we know, 'asymptotes are the lines that approaches the curves but does not meet them'.

As, the numerator of f(x) is of lower degree than the denominator.

We have, the function f(x) has x= 0 as the horizontal asymptote.

Further, graph of g(x) gives us, 'the line x= 4 is the asymptote'.

Hence, the function g(x) has vertical line x= 4 as the asymptote.