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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

Identify The Rational Function Whose Graph Is Given Below Note The Xintercept Of The Graph Is X4 And The Yintercept Of The Graph Is Y3 The Graph Has One Vertica class=

Sagot :

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

[tex]f(x) = -1.5\frac{(x - 4)}{x - 2}[/tex]

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:

[tex]f(x) = \frac{a(x - 4)}{x - 2}[/tex]

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

[tex]-3 = \frac{a(0 - 4)}{0 - 2}[/tex]

[tex]-4a = 6[/tex]

[tex]a = -1.5[/tex]

Thus, the function is:

[tex]f(x) = -1.5\frac{(x - 4)}{x - 2}[/tex]

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

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