In Exercises 95–98, use long division to rewrite the equation for...

Question

In Exercises 95–98, use long division to rewrite the equation for g in the form quotient + remainder/divisor. Then use this form of the function's equation and transformations of f(x) = 1/x to graph g. g(x)=(3x−7)/(x−2)

Accepted Answer

Rewrite the equation of F in the form of quotient plus remainder divided by supervisor using long division and graph the function using the equation of its function. And the transformation of one divided by X where we have F of X equals seven X minus eight, divided by X minus 13. We notice we have four different graphs as our possible answer. Now to solve this, we need to determine our long division. We have seven X minus eight divided by X minus 13 with long division. We can solve this by taking our first term in our quotient and divided by the first term of our divisor. So in other words, we have seven X divided by X which gives us seven on the top of our division, we'll put a seven, we can now multiply our new seven by our divisor X minus and put it underneath our quotient. We have seven X and then seven multiplied by 13 gives us negative 91. You are subtract these equations. Now seven X minus seven X gives us zero X native eight minus native 91 gives us plus 83. We can now rewrite our equation we want the form of quotient plus remainder divided by divisor. So quotient in this case is seven, our remainder is our 83 that's left over divided by our divisor X minus have the equation or our transformations. We can now determine our transformations as well. We have a plus seven outside away from our X that is empirical shift and naver will shift up by seven. We also have a horizontal shift based on our negative 13. Since we are negative, we will shift this to the right by 13. And finally, we have a vertical stretch of 83 based on the 83 in our numerator. If we look at our possible answers, we determine answer B is the answer for our graph has all of our transformations and the equation we created. OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

In Exercises 95–98, use long division to rewrite the equation for g in the form quotient + remainder/divisor. Then use this form of the function's equation and transformations of f(x) = 1/x to graph g. g(x)=(3x−7)/(x−2)

Key Concepts

Polynomial Long Division

Rational Functions

Transformations of Functions

Watch next