Graph Exponential Functions - Pre-Calculus
Card 0 of 7
Define a function 
as follows:
Give the 
-intercept of the graph of 
.
Define a function
Give the
The 
-coordinate ofthe 
-intercept of the graph of 
is 0, and its 
-coordinate is 
:
The 
-intercept is the point 
.
The
The
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What is the 
-intercept of 
?
What is the
The 
-intercept of a graph is the point on the graph where the 
-value is 
.
Thus, to find the 
-intercept, substitute 
and solve for 
.
Thus, we get:
The
Thus, to find the
Thus, we get:
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Which of the following functions represents exponential decay?
Which of the following functions represents exponential decay?
Exponential decay describes a function that decreases by a factor every time 
increases by 
.
These can be recognizable by those functions with a base which is between 
and 
.
The general equation for exponential decay is,
where the base is represented by 
and 
.
Thus, we are looking for a fractional base.
The only function that has a fractional base is,
.
Exponential decay describes a function that decreases by a factor every time
These can be recognizable by those functions with a base which is between
The general equation for exponential decay is,
Thus, we are looking for a fractional base.
The only function that has a fractional base is,
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Does the function 
have any 
-intercepts?
Does the function
The 
-intercept of a function is where 
. Thus, we are looking for the 
-value which makes 
.
If we try to solve this equation for 
we get an error.
To bring the exponent down we will need to take the natural log of both sides.
Since the natural log of zero does not exist, there is no exponent which makes this equation true.
Thus, there is no 
-intercept for this function.
The
If we try to solve this equation for
To bring the exponent down we will need to take the natural log of both sides.
Since the natural log of zero does not exist, there is no exponent which makes this equation true.
Thus, there is no
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Choose the description below that matches the equation:
Choose the description below that matches the equation:
Exponential graphs can either decay or grow. This is based on the value of the base of the exponent. If the base is greater than 
, the graph will be growth. And, if the base is less than 
, then the graph will be decay. In this situation, our base is 
. Since this is greater than 
, we have a growth graph. Then, to determine the y-intercept we substitute 
. Thus, we get:
for the y-intercept.
Exponential graphs can either decay or grow. This is based on the value of the base of the exponent. If the base is greater than
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Choose the description that matches the equation below:
Choose the description that matches the equation below:
Exponential graphs can either decay or grow. This is based on the value of the base of the exponent. If the base is greater than 
, the graph will be growth. And, if the base is less than 
, then the graph will be decay. In this situation, our base is 
. Since this is less than 
, we have a decay graph. Then, to determine the y-intercept we substitute 
. Thus, we get:
for the y-intercept.
Exponential graphs can either decay or grow. This is based on the value of the base of the exponent. If the base is greater than
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Which of the following represents the graph of 
?
Which of the following represents the graph of 
Note that the negative sign in this function comes outside of the parentheses. This should show you that the bigger the number in parentheses, the lower the curve of the graph will go. Since this is an exponential function, the larger that the x value gets, then, the "more negative" this graph will go. The graph closest to zero on the left-hand side - where x is negative - and then shoots down and to the right rapidly when x gets larger is the correct graph.
Note that the negative sign in this function comes outside of the parentheses. This should show you that the bigger the number in parentheses, the lower the curve of the graph will go. Since this is an exponential function, the larger that the x value gets, then, the "more negative" this graph will go. The graph closest to zero on the left-hand side - where x is negative - and then shoots down and to the right rapidly when x gets larger is the correct graph.
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