Function Problems (rev. 10/9/1998, 9/29/1999)

Dear Students,

Word problems involving functions can be hard. Wouldn’t it be great if we had a general method to solve them? Well, we do. I call it "Dep-Scribble-SWYK-E-A" and I hope it works for you, too.

Sincerely,

Mr. Hansen

Step

Description

Dep (Dependency)

What depends on what?

Scribble

Make a sloppy sketch showing the trend (up, down, whatever).

SWYK

Show (only) What You Know on a better sketch. For example:

  • known point(s) of the function
  • slope (if it’s a linear function)
  • x-intercept(s)
  • y-intercept

Note: Usually you will be given only a couple of these. Don’t bother trying to put everything on the sketch just yet.

E

Build an Equation.

A

Apply your equation to answer the question(s) posed. Usually this means plugging in x and solving for y, or plugging in y and solving for x.

Optional step: Rewrite your equation for the graphing calculator (Y1 = ______), and use the graph to refine your sketch. This is particularly valuable for complicated functions.

EXAMPLE

Joe needs to hire a plumber to fix a disastrous mess in his basement. The plumber charges $50 just to make the trip to Joe’s house, plus $75 per hour.

a) How much money will Joe have to pay if the job lasts 3 hours?

b) What if it lasts 4.5 hours?

c) How long can the plumber work if Joe has only $100 to spend?

SOLUTION (Fill these in based on the classroom discussion.)

DEP)

 

 

SCRIBBLE)

 

 

SWYK)

 

 

E)

 

 

A)