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# Write an equation for a rational function with: Vertical asymptotes at x = -2 and x = -6 x intercepts at x = 1 and x = -5 y intercept at 2

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Write an equation for a rational function with: Vertical asymptotes at x = -2 and x = -6 x intercepts at x = 1 and x = -5 y intercept at 2

y =______

Jun 11, 2015

#2
+101431
+10

The basic equation would be

y = [(x + 5)(x  - 1)] / [(x + 2) ( x + 6) ]

Note, however, that when x = 0, y = -5/12....but we need to have y = 2,  when x = 0.......this implies that, if we just multiipied the basic function by -24/5, this would produce what we want since (-5/12)(-24/5) = 2

So we have...

y = [-24(x + 5)(x  - 1)] / [5(x + 2) ( x + 6) ]  =  (-24x^2 - 96x + 120) / (5x^2 + 40x  + 60)

Here's the graph........https://www.desmos.com/calculator/pwcgxdimn5

Jun 11, 2015

#1
+22358
+10

Write an equation for a rational function with: Vertical asymptotes at x = -2 and x = -6 x intercepts at x = 1 and x = -5 y intercept at 2

$$y=\dfrac{\left(-4.8\right)\left(x+5\right)\left(x-1\right)}{\left(x+6\right)\left(x+2\right)}$$

Jun 11, 2015
#2
+101431
+10

The basic equation would be

y = [(x + 5)(x  - 1)] / [(x + 2) ( x + 6) ]

Note, however, that when x = 0, y = -5/12....but we need to have y = 2,  when x = 0.......this implies that, if we just multiipied the basic function by -24/5, this would produce what we want since (-5/12)(-24/5) = 2

So we have...

y = [-24(x + 5)(x  - 1)] / [5(x + 2) ( x + 6) ]  =  (-24x^2 - 96x + 120) / (5x^2 + 40x  + 60)

Here's the graph........https://www.desmos.com/calculator/pwcgxdimn5

CPhill Jun 11, 2015