Introduction to Exponential Functions
Introduction to Exponential FunctionsToday, we will be
investigating the similarities and/or differences between three
different types of graphs: y = 2x, y = 2x2, and y = 2x.
Ex.Graph the following functions using the table of values
provided. Also calculate the first and second differences for
each:
i)y = 2xii)y = 2x2iii)y = 2xxy1st diff.2nd diff.xy1st diff.2nd
diff.xy1st diff.2nd diff.
-3-3-3
-2-2-2
-1-1-1
000
111
222
333
a)Describe any similarities and/or differences you see for the
equations of the functions.
b)Describe any similarities and/or differences you see for the
graphs of the functions.
c)Describe any similarities and/or differences you see for the
finite differences of the functions.
SUMMARY PROPERTIES OF EXPONENTIAL FUNCTIONS1.An exponential
function is in the form ____________, where _____ is the base, and
_______ is the exponent.
2._________ always passes through the point ___________.
3.No matter how small you make x, y will _________________. The
graph will get
____________ and ___________ to the _____________, but will
never touch it.
Graphs of Exponential Functions, y = abx, a=1Ex.
Graph each of the following exponential functions using the
table of values provided on the same grid. Calculate the first and
the CONSTANT RATIO for each (the constant ratio is when you divide
consecutive first differences):
i)y = 2xii)y = 4xiii)y = 7xXY1st diff.Constant RatioXY1st
diff.Constant RatioXY1st diff.Constant Ratio
-2-2-2
-1-1-1
000
111
222
a)How are these graphs similar?
b)How are these graphs different?
c)What does the constant ratio tell you?
d)How does the value of the base affect your graph?
e)What is the domain and range for all the graphs?f)What is the
x-intercept for each graph?
g)All three graphs have one point in common. What is it?
Ex.
Graph each of the following exponential functions using the
table of values provided on the same grid. Calculate the first and
the constant ratio for each:i)y =
ii)y =
iii)y =
XY1st diff.Constant RatioXY1st diff.Constant RatioXY1st
diff.Constant Ratio
-2-2-2
-1-1-1
000
111
222
a)How are these graphs similar?
b)How are these graphs different?
c)What does the constant ratio tell you?
d)How does the value of the base affect your graph?
e)What is the domain and range for all the graphs?f)What is the
x-intercept for each graph?
g)All three graphs have one point in common. What is it?
DEFINTION:An
is a line that a curve approaches more and more closely, but
never crosses or touches it on some portion of its domain.
SUMMARY PROPERTIES OF y=abx, a=1A function in the form y=bx:
a)
if b>1
b)
if 0
