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): $(0,\frac{-1}{3})$, 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, $f(x)=\frac{1}{x-3}$ 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, $f(0)=\frac{1}{0-3}$ i.e. $f(0)=\frac{-1}{3}$.

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

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.

Answer 2

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