To me, a funcion is an equation for which any x that can be plugged into the equation will yield exactly one y out of the equation.
within this equation, there are two factors called the domain and range. the domain refers to the input for a function, while range refers to the output.
an inverse is where the x and y values for an equation are flipped/switched.
a composition is the process of combining two functions where one function is performed first and the result of which is substituted in place of each x in the other function.
#below is an example of domain
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domain= [2,4,6,8]
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f(x)= 2*x-5
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#below is an example of range
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[f(x) for x in domain]
[-1, 3, 7, 11] [-1, 3, 7, 11] |
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5 5 |
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#below are examples of domain and range
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domain = [-10..10]
[f(x) for (x) in domain]
[96, 77, 60, 45, 32, 21, 12, 5, 0, -3, -4, -3, 0, 5, 12, 21, 32, 45, 60, 77, 96] [96, 77, 60, 45, 32, 21, 12, 5, 0, -3, -4, -3, 0, 5, 12, 21, 32, 45, 60, 77, 96] |
range = [-10..10]
[f(x) for (x) in range]
[96, 77, 60, 45, 32, 21, 12, 5, 0, -3, -4, -3, 0, 5, 12, 21, 32, 45, 60, 77, 96] [96, 77, 60, 45, 32, 21, 12, 5, 0, -3, -4, -3, 0, 5, 12, 21, 32, 45, 60, 77, 96] |
#Below is an example of a composition
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f(x)= x+4
g(x)= x*5
g(f(x))
5*x + 20 5*x + 20 |
Traceback (click to the left of this block for traceback) ... SyntaxError: invalid syntax Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "_sage_input_19.py", line 10, in <module>
exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("aChmKGcoeCkpKT0="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
File "", line 1, in <module>
File "/tmp/tmp4ueRJX/___code___.py", line 2
h(f(g(x)))=
^
SyntaxError: invalid syntax
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f(x)= 5^x + 3
plot (f,1,13)
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f(x)= 7y-3
inverse of it
y=( f(x) + 3)/7
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