Question

1.Suppose you have a function such that the domain of is −4≤x≤2

and the range of is −1≤y≤6.

a. What is the domain and range of the transformation

f(2(x+3))?

b. What is the domain and range of the transformation

2f(x)−3?

c. How do you know your answers are correct?

d. What can we say about how transformations affect the domain and range of a function?

2. Suppose a local vendor charges $2 per hot dog and that the number of hot dogs sold per hour x is given by x(t)=−4t^2+20t+92, where t is the number of hours since 10 AM, 0≤t≤4

a. Find an expression for the revenue per hour R as a function of x.

b. Find and simplify (R∘x)(t). What does this represent?

c. What is the revenue per hour at noon?

d. If the price were raised to $3 per hot dog with no change in the x(t) equation, which hour would produce the most revenue? Why?

e. If the price were dropped to $1 per hot dog, but that price drop caused the number of sales to increase according to the function x(t)=−9t^2+22t+138, would the vendor make more money at the original $2 price, or at the $1 price?

3. Danielle makes the claim that when the polynomial x^2−3x−10 is divided by x−5, the remainder is 0. Use what you have learned about dividing polynomials to either verify that Danielle is correct or prove that she is incorrect. What arguments would you use to support your claim? Are there any other arguments? Justify your answers.

Answer 1