Homework: The Function Game
Name: __________________________
Date: _________________________
Exercise 1.1
Describe in words what a variable is, and what a function is.
There are seven functions below (numbered #2-8). For each function,
 Write the same function in algebraic notation.
 Generate three points from that function.
For instance, if the function were “Add five” the algebraic notation would be “x + 5”. The three points might
be (2, 7), (3, 8), and (-5, 0).
Exercise 1.2
Triple the number, then subtract six.
a. Algebraic notation:____________________
b. Three points:____________________
Exercise 1.3
Return 4, no matter what.
a. Algebraic notation:____________________
b. Three points:__________________________
Exercise 1.4
Add one. Then take the square root of the result. Then, divide that result into two.
a. Algebraic notation:____________________
b. Three points:__________________________
Exercise 1.5
Add two to the original number. Subtract two from the original number. Then, multiply those
two answers together.
a. Algebraic notation:____________________
b. Three points:__________________________
Exercise 1.6
Subtract two, then triple.
a. Algebraic notation:____________________
b. Three points:__________________________
Exercise 1.7
Square, then subtract four.
a. Algebraic notation:____________________
b. Three points:__________________________
Exercise 1.8
Add three. Then, multiply by four. Then, subtract twelve. Then, divide by the original number.
a. Algebraic notation:____________________
b. Three points:__________________________
Homework: The Function Game
Name: __________________________
Date: _________________________
Exercise 1.9
In some of the above cases, two functions always give the same answer, even though they are different
functions. We say that these functions are “equal” to each other. For instance, the function “add three and
then subtract five” is equal to the function “subtract two” because they always give the same answer. (Try
it, if you don't believe me!) We can write this as:
x+3–5=x–2
Note that this is not an equation you can solve for x, it is a generalization which is true for all x values. It is
a way of indicating that if you do the calculation on the left, and the calculation on the right, they will
always give you the same answer.
In the functions #2-8 above, there are three such pairs of “equal” functions. Which ones are they? Write
the algebraic equations that state their equalities (like my x + 3 – 5 = x – 2 equation).
Exercise 1.10
Of the following sets of numbers, there is one that could not possibly have been generated by any
function whatsoever. Which set it is, and why? (No credit unless you explain why!)
a. (3, 6), (4, 8), (–2, –4)
b. (6, 9), (2, 9), (–3, 9)
c. (1, 112), (2, –4), (3, 3)
d. (3, 4), (3, 9), (4, 10)
e. (–2, 4), (–1, 1), (0, 0,) (1, 1), (2, 4)