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With a table of value, you first make sure the change in x is constant. Then you look at the ratio of the y's value. If the ratio of the values is the same, then it is an exponential function:
x y
1 120
2 180
3 270
4 405
5 607.5
6 911.25
e.g. 180/120 = 1.5, 270/180 = 1.5, 405/270 = 1.5
Therefore, this is an exponential function. To take the question even further, we can even identify the equation of the exponential function.
y=Ar^x (*note: ^ is the symbol for "to the power of")
A = the first term when x is 0
r = the constant ratio
To find A, we sub in one of the coordinates in the table of value. I choose the coordinate (1, 120).
120 = A(1.5^1)
120/1.5 = A
80 = A
Therefore the equation is: y = 80(1.5^x)
Hope this helps.
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What are some characteristics of the graph of an exponential function?
An exponential function is a nonlinear function in the form y=ab^x, where a isn't equal to zero. In a table, consecutive output values have a common ratio. a is the y-intercept of the exponential function and b is the rate of growth/decay.
What advantages can you see of having a function rule instead of a table of values?
A table of values is no use if the domain is infinite.
A logarithmic function takes the exponential function's and returns the exponential function's input?
output
Is an exponential function is the inverse of a logarithmic function?
No, an function only contains a certain amount of vertices; leaving a logarithmic function to NOT be the inverse of an exponential function.
How can you identify exponential function from its graph?
The exponential function - if it has a positive exponent - will grow quickly towards positive values of "x". Actually, for small coefficients, it may also grow slowly at first, but it will grow all the time. At first sight, such a function can easily be confused with other growing (and quickly-growing) functions, such as a power function.
What are some characteristics of the graph of an exponential function?
An exponential function is a nonlinear function in the form y=ab^x, where a isn't equal to zero. In a table, consecutive output values have a common ratio. a is the y-intercept of the exponential function and b is the rate of growth/decay.
Are there points of discontinuity for exponential functions?
There are no points of discontinuity for exponential functions since the domain of the general exponential function consists of all real values!
A function takes the exponential function's output and returns the exponential function's input?
A __________ function takes the exponential function's output and returns the exponential function's input.
What is the definition to function table?
a table used to show values of the variable expression for a given function
What advantages can you see of having a function rule instead of a table of values?
A table of values is no use if the domain is infinite.
What is the parent function for the exponential function?
The parent function of the exponential function is ax
Is the inverse of an exponential function the quadratic function?
No. The inverse of an exponential function is a logarithmic function.
What function searches for a specific value in a table and returns that values relative position from the table not the value itself?
The MATCH function.
What is the Definition to function?
a table used to show values of the variable expression for a given function
A logarithmic function takes the exponential function's and returns the exponential function's input?
output
A logarithmic function takes the exponential function's output and returns the exponential function's?
input
What are the three views of a function?
rule, table of values and graph
