Question

Identify the rational function whose graph is given below. Note the x-intercept of the graph is x=4 and the y-intercept of the graph is y=−3. The graph has one vertical asymptote at x=2

Answer 1

Using the vertical asymptote of the function, it is found that it is given by:

$f(x) = -1.5\frac{(x - 4)}{x - 2}$

What are the asymptotes of a function f(x)?

• The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.

• The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.

In this problem, the x-intercept of the graph is x=4, hence the numerator is a(x - 4).

The graph has one vertical asymptote at x=2, hence the denominator is x - 2.

Hence:

$f(x) = \frac{a(x - 4)}{x - 2}$

The y-intercept of the graph is y=−3, hence:

$-3 = \frac{a(0 - 4)}{0 - 2}$

$-4a = 6$

$a = -1.5$

Thus, the function is:

$f(x) = -1.5\frac{(x - 4)}{x - 2}$

More can be learned about asymptotes at brainly.com/question/16948935