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Introduction (P)
Rule Use parentheses ( and ) to
maintain order of operations
with fractions and exponents.
Note Use the 2nd ANS key to recall
the result of the last operation.
Note Use the 2nd ENTRY key to recall
the last set of keystrokes.
Rule Solve percent change problems
using the formula:
change % change

initial
100
Functions and Models (1.1)
Def’n A function describes a relationship
between inputs and an output.
Def’n A model uses a function to describe
a real situation or process.
Rule Functions can be represented
algebraically, numerically,
graphically, or verbally.
Formulas (1.1)
Def’n A formula describes a function
using numbers, letters, and symbols.
Def’n When equation notation is used,
the output variable is represented
by only a letter.
Def’n When function notation is used,
the output variable makes reference
to the input variable(s).
Tables (1.2)
Def’n A table describes a function using
columns of input and output values.
Rule When estimating an output value
for an input value halfway between
two table values, average the two
corresponding output values.
Average Rate of Change (1.2)
Def’n The average rate of change of a
function is the difference in the
output variable divided by the
difference in the input variable.
AROC 
 output
 input
Def’n A limiting value exists whenever
output values level off while input
values continue to rise.
Graphs (1.3)
Def’n A graph describes a function using a
two-dimensional picture with labels
and headings.
Def’n A graph is increasing if it rises from
left to right, and decreasing if it falls
from left to right.
Def’n The minimum is the lowest output
value, and the maximum is the
highest output value.
Concavity (1.3)
Def’n A graph is concave up if its ends are
are bent upward, and concave down
if its ends are bent downward.
Def’n An inflection point occurs where
concavity changes from up to down
or from down to up.
Creating Tables in the TI-83 (2.1)
 Type an equation into Y1 using
the Y= key.
 Select the table features using
the 2nd TBLSET key.
 View the table using the
2nd TABLE key.
Features of TI-83 Tables (2.1)
Rule Find limiting values by setting
Tbl  1000 .
Rule Find input values, minimum
values, or maximum values by
setting Tbl  0.01.
Creating Graphs on the TI-83 (2.2)
 Type an equation into Y1 using
the Y= key.
 Select the viewing area for the
graph using the WINDOW key.
 View the graph using the GRAPH key.
Features of TI-83 Graphs (2.2, 2.4, 2.5)
Rule Calculate output values using the
2nd CALC value feature.
Rule Find limiting values or inflection
points using the TRACE key.
Rule Calculate input values using the
2nd CALC intersect feature.
Rule Locate minimum values using the
2nd CALC minimum feature.
Rule Locate maximum values using the
2nd CALC maximum feature.
Slope (3.1)
Def’n The slope m of a line is the ratio of
the vertical change between any two
points on the line to the horizontal
change between the same two points:
m
y rise

x run
Note The slope formula can be rearranged
to solve for y or
x
y  m  x
as follows:
x 
y
m
Linear Functions (3.2, 3.3)
Def’n A linear function is a function with
a constant rate of change.
Rule A linear function can be written as
y  mx  b , where m is the AROC
and b is the initial value.
Finding Linear Equations (3.2, 3.3)
Rule If the slope m and one data point (x , y )
are given, plug the values into the
equation y  mx  b and solve for b.
Rule If two data points are given, first
calculate the slope m, then plug in
and solve for b as above.
Def’n The vertical intercept is the output
value when the input is zero, and
the horizontal intercept is the input
value when the output is zero.
Modeling Nearly Linear Data (3.4)
Rule Model data that are nearly linear
using a method called least-squares
linear regression.
 Type the input values into L1 and
the output values into L2 using the
STAT EDIT feature.
 Calculate the line of best fit using
the STAT CALC LinReg(axb)
feature.
 View the graph of the points and the
line using the 2nd STATPLOT key.
Solving Linear Systems (3.5)
Rule Solve linear systems by:
(1) writing two equations from words,
(2) solving both equations for the
same variable,
(3) typing the equations into Y1
and Y2, and
(4) locating the intersection of the
graphs of the equations using the
2nd CALC intersect feature.
Exponential Functions (4.1)
Def’n An exponential function is
a function with a constant
percentage rate of change.
Rule An exponential function can
be written as y  a  b x , where
a is the initial value and b is
the growth or decay factor.
Growth and Decay (4.1)
Rule A factor greater than one indicates
growth, while a factor less than one
indicates decay.
Def’n The growth or decay rate r is given
by: r  b  1.
Rule The growth or decay factor for
a time period of k units is bk.
Finding Exponential Equations (4.2)
Rule If the growth or decay factor b and
and one data point (x , y ) are given,
plug the values into the equation
y  a  b x and solve for a.
Rule If two data points are given, first
calculate the factor b  (y2 y1 )(1 x ) ,
then plug in and solve for a as above.
Exponential Regression (4.3)
Rule Model data that are nearly exponential
using exponential regression.
Logarithmic Functions (4.5)
Rule If y is an exponential function of x,
then x is a logarithmic function of y.
Def’n If y  b x , then x is the base b
logarithm of y, written as x  logb y .
Def’n If y  10x , then x is the common
logarithm of y, written as x  log y .
Def’n If y  e x , then x is the natural
logarithm of y, written as x  ln y .
The Exponential Connection (4.5)
Rule If y is an exponential function of x,
then ln y is a linear function of x.
Rule Data that are nearly exponential can
be transformed and modeled using
linear regression as follows:
L 3  ln(L 2 )
LinReg L1, L 3, Y1
Logarithmic Applications (4.4)
Size of an Earthquake:
P 
R  R 0  log 
 P0 
Loudness of Sound:
I 
D  D0  10  log 
 I0 
Brightness of Light:
 I 
M  M 0  2.5  log 
 I0 
Power Functions (5.2)
Def’n A power function is a function with
an output that is proportional to a
power of the input.
Rule A power function can be written as
y  a  x b , where a is a constant and
b is the power.
Rule If the input is multiplied by k, then
the output is multiplied by kb.
Power (5.2)
Rule If b  1, the function is
increasing and concave up.
If 0  b  1, the function is
increasing and concave down.
If b  0 , the function is
decreasing and concave up.
Finding Power Equations (5.2)
Rule If the power b and one data point
(x , y ) are given, plug the values into
the equation y  a  x b and solve for a.
Rule If two data points are given, first
calculate the power b 
ln(y2 y1 )
,
ln(x 2 x1 )
then plug in and solve for a as above.
Power Regression (5.3)
Rule Model data that are nearly power
using power regression.
Rule If y is a power function of x, then
ln y is a linear function of ln x.
Rule Data that are nearly power can be
transformed and modeled using
linear regression as follows:
L 3  ln(L 2 ) L 4  ln(L1) LinReg L 4, L 3, Y1