Question

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 help you visualize f(x).

Answer 1

A) f(x): y-intercept is
`(0,(-1)/(3))` and g(x): y-intercept is (0,0)

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

Explanation:

We are given the functions,
`f(x)=(1)/(x-3)` 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,

`f(0)=(1)/(0-3)` i.e.
`f(0)=(-1)/(3)`.

Thus, the y-intercept of the function f(x) is the point
`(0,(-1)/(3))`.

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
`f(x)=(1)/(x-3)` 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).