Question

Write an equation for a rational function with:

Answer 1

The equation for a rational function with: Vertical asymptotes at x = 2 and x = -4. x-intercepts at x = 1 and x = 4. y-intercept at 9 is

$y=-36\frac{(x - 1) (x - 4)}{(x - 2) (x +4)}$

How to determine the equation for a rational function

information gotten from the question

From the question given above, the following data were obtained:

• Vertical asymptotes at x = 2 and x = -4
• x-intercepts at x = 1 and x = 4
• y-intercept at 9
• y =?

Rational function means that the equation will be a fraction

The rational function that models the Vertical asymptotes at x = 2 and x = -4. x-intercepts at x = 1 and x = 4. y-intercept at 9 is written as follows

The numerator

x-intercepts at x = 1 and x = 4

x = 1   ⇒  (x - 1)

x = 4   ⇒  (x - 4)

This means the equation will have (x - 1) (x - 4) as the numerator

The denominator

Vertical asymptotes at x = 2 and x = -4

x = 2   ⇒  (x - 2)

x = -4   ⇒  (x + 4)

This means the equation will have (x - 2) (x + 4) as the denominator

y-intercept at 9

expressing the functions derived already gives

$y=a\frac{(x - 1) (x - 4)}{(x - 2) (x +4)}$

substituting x = 0 and y = 9 and solving  gives a

$9=a\frac{(0 - 1) (0 - 4)}{(0 - 2) (0 +4)}$

$9=a\frac{(4)}{(-8)}$

4a = 9 * -8

a = -36

The equation of the rational function is $y=-36\frac{(x - 1) (x - 4)}{(x - 2) (x +4)}$

Learn more on  equation for a rational function at :

brainly.com/question/28032338

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