Chris is 1½ years younger than his brother David. Let DD represent David’s age, and CC represent Chris’s age.

Sally slips into a broom closet, waves her magic wand, and emerges as…the candy bar fairy! Flying through the window of the classroom, she gives every student two candy bars. Then five candy bars float through the air and land on the teacher’s desk. And, as quickly as she appeared, Sally is gone to do more good in the world.

Let ss represent the number of students in the class, and cc represent the total number of candy bars distributed. Two for each student, and five for the teacher.

The function f ( x ) = f ( x ) = size 12{f \( x \) ={}} {} is “Subtract three, then take the square root.”

The function y(x)y(x) is “Given any number, return 6.”

z ( x ) = x 2 − 6x + 9 z ( x ) = x 2 − 6x + 9 size 12{z \( x \) =x rSup { size 8{2} } - 6x+9} {}

Of the following sets of numbers, indicate which ones could possibly have been generated by a function. All I need is a “Yes” or “No”—you don’t have to tell me the function! (But go ahead and do, if you want to…)

Make up a function involving music.

Here is an algebraic generalization: for any number x x size 12{x} {} , x2−25=(x+5)(x−5)x2−25=(x+5)(x−5) size 12{x rSup { size 8{2} } - "25"= \( x+5 \) \( x - 5 \) } {}.

Amy has started a company selling candy bars. Each day, she buys candy bars from the corner store and sells them to students during lunch. The following graph shows her profit each day in March.

Figure 1

The picture below shows the graph of y=xy=x size 12{y= sqrt {x} } {}. The graph starts at (0,0)(0,0) size 12{ \( 0,0 \) } {} and moves up and to the right forever.

Figure 2

The following graph represents the graph y=f(x)y=f(x) size 12{y=f \( x \) } {}.

Figure 3

Figure 4

Figure 5