Find the x and yintercepts of the rational function. (If an answer does not ex
Algebra

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Find the x and yintercepts of the rational function. (If an answer does not exist, enter DNE.)
x^{2} − 2x − 24 
x − 7 
xintercept  (x, y) =  (smaller xvalue)  
xintercept  (x, y) =  (larger xvalue)  
yintercept  (x, y) = 
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In order to find the xintercepts we make t(x) zero and we solve for x like this.
t(x) = (x^2  2x  24)/(x7) > 0 = (x^2  2x  24)/(x7) > 0*(x7) = (x7)*(x^2  2x  24)/(x7)
0 = x^2  2x  24 > x^2  2x  24 = 0. This is a quadratic equation that we can solve by factoring. For that, we find two numbers that their product is  24 and their algebraic addition give  2. Then the numbers would be:
6 and 4 since (6)(4) =  24 and  6 + 4 = 2. Then it would factor like this:
x^2  2x  24 = 0 > (x  6)(x + 4) = 0. So we equal each factor to zero and solve for x.
x  6 = 0 > x  6 + 6 = 0 + 6 > x = 6
x + 4 = 0 > x + 4  4 = 0  4 > x =  4
Then we write the oredered pairs (x , y) which are: (6 , 0) and ( 4, 0)
On the other hand, in order to find the yintercept we make the x zero like this.
t(x) = (x^2  2x  24)/(x7) > t(0) = (0^2  2(0)  24)/(07) > t(0) = (0  0  24)/(0 7)
t(0) = 24/7 > t(0) = 24/7. Finally, we write the ordered pair (x ,y) which is: (0 , 24/7)
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