The amount of food that cats typically eat increases as their weight increases. A rational function that describes this is

F(x) = 12x x+5

where the amount of food is given in ounces and the weight of the cat, x is given in pounds. Calculate the horizontal asymptote. How many ounces of food will most adult cats eat?

A. 12 oz.
Correct! As x increases to infinity, F(x) approaches 12.

B. 5 oz.
Incorrect. Examine the table or the graph associated with this function. What happens to y as x gets larger and larger?

C. 6 oz.
Incorrect. Examine the table or the graph associated with this function. What happens to y as x gets larger and larger?

D. 2.4 oz.
Incorrect. Examine the table or the graph associated with this function. What happens to y as x gets larger and larger?

The intensity of a light varies inversely with the square of the distance to the light. For a particular bulb, the intensity is modeled by the equation, I = 1080 d2 . At what distance (in meters) will the intensity be 100 units?

A. 10.8 m.
Incorrect. Remember to take the square root when solving for d.

B. 0.01 m.
Incorrect. While this is the inverse of 100, it is not the solution to this question.

C. 3.286 m.
Correct! You could have solved this graphically on your calculator.

D. 0.108 m.
Incorrect. Substitute 100 for I.

The new principal of a large high school tries to learn students’ names. The number of names she can remember, N(t), increases with each week in the year t and is given by the rational function:

N(t) = 600t t+20

According to this function, what are the most names she can remember?

A. 600
Correct! As t gets very large, N(t) approaches 600.

B. 20
Incorrect. Examine the table or graph; determine what happens to N(t) as t gets very large.

C. 30
Incorrect. Examine the table or graph; determine what happens to N(t) as t gets very large.

D. 1200
Incorrect. Examine the table or graph; determine what happens to N(t) as t gets very large.

Jorge purchased a microwave oven for $597. The rational equation calculating the total monthly cost, C(n), of operating the microwave is C(n) = 597+15n      n , where n is the total number of years the microwave lasts. Find the vertical and horizontal asymptotes and state whether or not the domain is the same as the relevant domain for the microwave.

  1. n = 0, C = 15,
    The domains are the same.
  2. n = 0, C = 15,
    The domains are different.
  3. n = 15, C = 0,
    The domains are the same.
  4. n = 15, C = 0,
    The domains are different.

A
Incorrect. The asymptotes are correct. The microwave has a lifespan that is greater than zero.

B
Correct! Since the function is undefined at n=0, one asymptote is n=0. Rewrite the equation as C(n)=597/n + 15 as it is easier to see the vertical asymptote. The microwave only has a positive lifespan.

C
Incorrect. The asymptotes are incorrect and the microwave has a lifespan that is greater than zero.

D
Incorrect. The asymptotes are reversed.