Try one of those:
15.Rock climbing routes are rated on a numbered scale with the highest number
representing the most difficult route. Sally tried a range of shoe sizes on each of several
routes of varying difficulty and found that when she wore smaller shoes, she could
climb routes of greater difficulty. If D represents the difficulty rating of a route Sally
successfully climbed and s represents the size of the shoes she wore on such a route,
then which of the following could express D as a function of s ?
A) D(s) = s^2
B) D(s) =
C) D(s) = s – 3.5D) D(s) = Here’s How to Crack It
Start by thinking about the relationship described in the question: the smaller the shoes, the greater the
difficulty. This is an inverse relationship. So, look for an inverse function. Only (D) is an inverse
function.
If you aren’t sure, try plugging in numbers to try it out. Plug in s = 8 then s = 10 to see if the result for D is
smaller when you use a larger shoe size. Since only (D) results in a smaller difficulty for a larger shoe
size, the correct response is (D).
WHAT’S THE POINT?
Why did math folks come up with functions? To graph them of course! When you put in a value for x, and
your machine (or function) spits out another number, that’s your y. You now have an ordered pair.
Functions are just another way to express graphs. Knowing the connection between functions and graphs
is useful, because you will most likely see questions involving graphs on the SAT.
The Coordinate Plane
A coordinate plane, or the “xy-plane,” is made up of two number lines that intersect at a right angle. The
horizontal number line is called the x-axis, and the vertical number line is the y-axis.
The four areas formed by the intersection of the axes are called quadrants. The location of any point can
be described with a pair of numbers (x, y), just the way you would point on a map: (0, 0) are the
coordinates of the intersection of the two axes (also called the origin); (1, 2) are the coordinates of the
point one space to the right and two spaces up; (–1, 5) are the coordinates of the point one space to the
left and five spaces up; (–4, –2) are the coordinates of the point four spaces to the left and two spaces
down. All these points are located on the diagram below.