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Find the equation
PLEASE HELP QUICK

Find the equation PLEASE HELP QUICK-example-1
User VikR
by
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1 Answer

5 votes

Answer:


y=(1)/(x-4)-2

Explanation:

The given graph represents a rational function with specific characteristics:

  • Vertical asymptote: x = 4
  • Horizontal asymptote: y = -2
  • x-intercept = (4.5, 0)

The shape of the curve resembles a reciprocal function in the form of


y=(a)/(x-h)+k

where:

  • x = h is the vertical asymptote.
  • y = k is the horizontal asymptote.
  • a is a constant.

As the vertical asymptote is x = 4, then h = 4.

As the horizontal asymptote is y = -2, then k = -2.

Substituting these values into the equation, we get:


y=(a)/(x-4)-2

To find the value of a, we can substitute the point on the curve (4.5, 0) into the equation and solve for a:


0=(a)/(4.5-4)-2


2=(a)/(0.5)


1=a

Finally, substituting the value of a = 1 back into the equation, we can write the equation of the graphed curve as:


\large\boxed{\boxed{y=(1)/(x-4)-2}}

Find the equation PLEASE HELP QUICK-example-1
User Wickjon
by
8.4k points

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