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

a) compare the y-intercepts of f(x) and g(x). use complete sentences.

b) compare the vertical asymptotes of f(x) and g(x). use complete sentences.

note: points will be deducted for not answering in complete sentences. you may use a graphing calculator to you visualize f(x).

A) f(x): y-intercept is and g(x): y-intercept is (0,0)

B) f(x): asymptote is x= 0 and g(x): asymptote is x= 4.

Step-by-step explanation:

We are given the functions, and g(x) graphed.

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

That is, 'y-intercepts are obtained when x= 0'.

So, we have,

i.e. .

Thus, the y-intercept of the function f(x) is the point .

Furhter, from the graph of g(x), we see that,

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

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

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

Since, the function has a numerator of lower degree than the denominator.

Thus, x= 0 is the horizontal asymptote of the function f(x).

Also, from the graph of g(x), we see that, The line x= 4 is approaching the curve infinitely.

Thus, the vertical line x= 4 is the asymptote of the function g(x).

step-by-step explanation: