Algebraic Expression Notes
Types of Algebraic Expressions:
 Inverse – x increases as y decreases, two separate opposite curves, doesn’t have a
pattern in table
 Linear – straight line, has a pattern in table
 Quadratic – parabola (“u” or “n” shape), doesn’t have a pattern in table
 Cubic – “s” or snake shaped graph, doesn’t have a pattern in table
 Exponential – one curve that flattens, has a pattern in the table
Steps setting up and finding algebraic expression using calculator:
1. In calculator go to “stat” and “edit”
2. Enter x’s in L1 and y’s in L2
3. To graph make sure “plot 1” is on (highlighted in “y=”)
4. If you cannot see all points use “zoomstat”
5. Look at patterns in table and shape of graph to determine the type of expression
6. Once you know which expression go to “stat” and “calc” to choose the appropriate
expression (like “linreg” for the linear function)
*The only exception is the inverse function – find the constant of variation to write
the inverse equation
7. To double check type equation in “y=” and graph, the line should go through all
points
Example 1:
x
f(x)
1
30
2
15
– 15
1 · 30 = 30
2 · 15 = 30
3 · 10 = 30
5 · 6 = 30
3
10
–5
5
6
This table shows x increasing and y
decreasing and no pattern, the first
option to look at is inverse
Since all points multiply together to
be a constant number, the function
has to be inverse with a constant of
variation of 30
This means the inverse equation is:
𝑓(𝑥) =
30
𝑥
Example 2:
x
f(x)
1
3
2
5
+2
3
7
+2
4
9
This table shows a pattern, meaning it
has to be linear or exponential
Graph the points to see the pattern
(using the steps above)
+2
Looking at the graph we see that the
points make a straight line, this means
the function is linear
Using “linreg” the calculator shows
the equation is: f(x) = 2x + 1
Example 3:
x
f(x)
2
0
3
2
+2
4
6
+4
5
12
This table shows no pattern and not
the inverse pattern, so it has to be
quadratic or cubic
+6
Looking at the graph we see that the
points make a curve and are fairly
close together, this means the
function is quadratic. If you are
unsure try both cubic and quadratic
and look at which equation fits the
points best.
Using “quadreg” the calculator shows
the equation is: 𝑓(𝑥) = 𝑥 2 − 3𝑥 + 2
Example 4:
x
f(x)
1
2
2
1
÷2
3
.5
÷2
4
.25
÷2
This table shows a pattern, meaning it
has to be linear or exponential
Graph the points to see the pattern
(using the steps above)
Looking at the graph we see that the
points make a curving line, this means
the function is exponential
Using “expreg” the calculator shows
the equation is: 𝑓(𝑥) = 4(.5)𝑥
Example 5:
x
f(x)
1
-1
2
2
+3
3
17
+ 15
4
50
This table shows no pattern and not
the inverse pattern, so it has to be
quadratic or cubic
+ 33
Looking at the graph we see that the
points make a curve and the numbers
are increasing by larger amounts, the
larger amounts suggests to try cubic
first. If you are unsure try both cubic
and quadratic and look at which
equation fits the points best.
Using “cubicreg” the calculator shows
the equation is: 𝑓(𝑥) = 𝑥 3 − 4𝑥 + 2