Question

Saul’s Chapeau Shop sells sleek sombreros
Saturdays and Sundays. The hats come in a variety
of sizes. The starting hat size has a diameter of
10 inches, and costs $4.00 . Each extra inch of brim
added to the diameter of the hat costs $0.75. The
largest diameter hat a customer can purchase is 48
inches.

Let c(x) represents the cost of a hat, where x
represents how many inches greater than 10
the diameter is. Saul is having a sale where all of
his hats are half off, given by the function h(x ).
Which of the following are true with regards to
h(x ):
I. The y-intercept is one-half the y-intercept of
c(x ).
II. The slope is one-half the slope of c(x)
III. The maximum value is one-half the
maximum value of c(x ).
a. I only
b. II only
c. III only
d. I and II only
e. I, II, and III

Answer 1

So is it true that h(x) = 1/2*[c(x)]? If so then E is the correct answer.

Answer 2

Or is there a trap hidden somewhere here?

Answer 3

oh and this information is also for this question :
Saul’s Chapeau Shop sells sleek sombreros
Saturdays and Sundays. The hats come in a variety
of sizes. The starting hat size has a diameter of
10 inches, and costs $4.00 . Each extra inch of brim
added to the diameter of the hat costs $0.75. The
largest diameter hat a customer can purchase is 48
inches.

Answer 4

Because x represents how many inches greater than 10 the diameter is, the 10 inch hat has x = 0. That hat costs $4 so 4 is the y-intercept (i.e. the value of y at x = 0).

But still, these info do not affect the relationship between h(x) and c(x) right?

Answer 5

ok so the answer is "e"