91Ó°ÊÓ

In \(23-28,\) write an equation of the direct variation described. The distance in miles, \(d\) , that Mr. Spencer travels is directly proportional to the length of time in hours, \(t,\) that he travels at 35 miles per hour.

For the parabola whose equation is \(y=a x^{2}+b x+c,\) the equation of the axis of symmetry is \(x=\frac{-b}{2 a}\) . The turning point of the parabola lies on the axis of symmetry. Therefore its \(x\) -coordinate is \(\frac{-b}{2 a}\) . Substitute this value of \(x\) in the equation of the parabola to find the \(y\) -coordinates of the turning point. Write the coordinates of the turning point in terms of \(a, b,\) and \(c .\)

A candy store sells candy by the piece for 10 cents each. The amount that a customer pays for candy, \(y,\) is a function of the number of pieces purchased, \(x .\) a. Describe, in set-builder notation, the cost in cents of each purchase as a function of the number of pieces of candy purchased. b. Yesterday, no customer purchased more than 8 pieces of candy. List the ordered pairs that describe possible purchases yesterday. c. What is the domain for yesterday's purchases? d. What is the range for yesterday's purchases?

Let \(c(x)\) represent the cost of an item, \(x,\) plus sales tax and \(d(x)\) represent the cost of an item less a discount of \(\$ 10 .\) a. Write \(c(x)\) using an 8\(\%\) sales tax. b. Write \(\mathrm{d}(x)\) c. Find \(c \circ \mathrm{d}(x)\) and \(\mathrm{d} \circ \mathrm{c}(x) .\) Does \(\mathrm{c} \circ \mathrm{d}(x)=\mathrm{d} \circ \mathrm{c}(x) ?\) If not, explain the difference between the two functions. When does it makes sense to use each function? d. Which function can be used to find the amount that must be paid for an item with a \(\$ 10\) discount and 8\(\%\) tax?

In \(23-28,\) write an equation of the direct variation described. Water is flowing into a swimming pool at the rate of 25 gallons per minute. The number of gallons of water in the pool, \(g,\) is directly proportional to the number of minutes, \(m,\) that the pool has been filling from when it was empty.

In \(23-28,\) write an equation of the direct variation described. At \(9 : 00\) A.M., Christina began to add water to a swimming pool at the rate of 25 gallons per minute. When she began, the pool contained 80 gallons of water. Christina stopped adding water to the pool at \(4 : 00\) P.M. Let \(g\) be the number of gallons of water in the pool and \(t\) be the number of minutes that have past since 9\(\cdot 00\) A.M. a. Write an equation for \(g\) as a function of \(t .\) b. What is the domain of the function? c. What is the range of the function? d. Is the function one-to-one? e. Is the function an example of direct variation? Explain why or why not.