Tutor profile: Laura Q.

How can you determine whether a rational function has a horizontal asymptote?

Once the numerator and denominator of the rational function have been written in standard form you need to find the exponents of the leading terms in both. If the leading exponent of the numerator is smaller than the leading exponent of the denominator than there will be a horizontal asymptote at y = 0. If the leading exponents are the same there will be a horizontal asymptote at the line y = a/b where a is the leading coefficient of the numerator and b is the leading coefficient of the denominator. If the leading exponent of the numerator is bigger than the leading exponent of the denominator then there is no horizontal asymptote and you should look for an oblique asymptote.

A ladder leaning against the wall makes an angle of 60 degrees with the ground. If the foot of the ladder is 6.5 feet from the wall, how high on the wall is the ladder?

Since the ladder leaning against the wall and the ground create a 30-60-90 degree triangle with the shorter side being the distance from the wall to the base of the ladder, we can use 30-60-90 properties to know that the longer leg (in this case the height on the wall of the ladder) is the shorter leg multiplied by the square root of 3.

Shopping online you order some items at $11.00 each. They charge you $20.00 for shipping so your total comes to $75.00, how many items did you order?

Using the equation C = 11.00c + 20 where C is the total cost, 11.00 is the cost of each item individually, c is the number of items, and 20 is the cost of shipping you can substitute 75 for C and use basic operations to solve for c. Your first step would be to subtract 20 from both sides leaving you with 55 = 11.00c. Then dividing both sides by 11.00 you would find that c=5 so you ordered 5 items.