Library of Functions

Perry Currin

1- f(x) = x^2

  • The domain of this fxn includes the set of all reals.
  • The range of this fxn includes y values greater than or equal to 0.
  • The Zero (when f(x)=0) of this fxn is 0 ;(0,0).
  • The fxn is symmetric with respect to the x axis
  • The function is not periodic
  • This function is not a one-to-one function.

2- f(x) = x^3

  • The domain of this function includes the set of all real numbers.
  • The range of this function includes the set of all real numbers
  • The zero (when f(x) = 0 ) of this function is 0 ;(0,0).
  • The graph of the function is symmetric with respect to the origin.
  • The function is considered odd.
  • The function is not considered periodic.
  • The function is considered a one-to-one function, meaning that only one x value exists for every f(x) value.

3- f(x) = abs(x)

  • The domain of this function includes the set of all real numbers.
  • The range of this function is the set of all real numbers greater than or equal to zero.
  • The zero (when f(x)= 0) of this function is 0 ;(0,0).
  • The graph of the function is symmetric with respect to the y axis.
  • The function is considered even.
  • This function is not periodic.
  • The function is not one-to-one. There are two x values for every (f(x)) value.

4-f(x) = sin x

  • The domain of this function includes the set of all real numbers.
  • The range of this function includes the set of all real numbers between and including 1 and -1.
  • There are an infinite number of zeros for this function. Zeros are listed as k*(pi) when k is an integer.
  • Graphically, this function is symmetric with respect to the origin.
  • This function is considered an odd function. f(-x) = -f(x)
  • The function is periodic and the period is 2*(pi).
  • The function is not considered a one-to-one function. There are an infinite number of x values for every f(x) value.

5- cos x

  • The domain of this function is the set of all real numbers.
  • The range of this function is the set of all real numbers between and including 1 and -1.
  • There are an infinite amount of zeros for this function. Zeros are listed as k*(pi)/2 where k is an odd integer.
  • Graphically, the function is symmetric with respect to the y axis.
  • The function is considered even. (f(-x) = f(x))
  • The function is periodic and the period is 2*(pi).
  • The function is not considered to be a one-to-one function. There are an infinite number of x values for every f(x) value.

6- tan x

  • The domain of this function is the set of all real numbers except for k*(pi)/2, k being any odd integer.
  • The range of this function is the set of all real numbers.
  • There are an infinite number of zeros associated with this function. These zeros are listed as k*(pi), k being any integer.
  • Graphically, this function is symmetric with respect to the origin.
  • The function is considered odd (f(-x) = -f(x)).
  • The function is periodic and the period is (pi).
  • The function is not considered to be a one-to-one function. There are an infinite number of x values for every f(x) value.

7- sec x

  • The domain of this function is the set of all real numbers except for k *(pi)/2, k being an odd integer.
  • The range of this function is the set of all real numbers except for those in between (but not including) -1 and 1.
  • There are no zeros associated with this function. Its graph never comes in contact with the x axis.
  • Graphically, the function is symmetric with respect to the y axis.
  • The function is considered to be even (f(-x) = f(x)).
  • The function is periodic, and the period is 2*(pi).
  • The function is not considered to be a one-to-one function. There are an infinite amount of x values for every f(x) value.

8 - f(x) = 2^x

  • The domain of this function is the set of all real numbers.
  • The range of this function is the set of all real numbers greater than 0.
  • There are no zeros for this function. The Graph does not come in contact with the x-axis.
  • Graphically, this function is symmetric to neither the y-axis nor the origin.
  • This function is considered neither even nor odd.
  • This function is not periodic.
  • There is only one x value for every f(x) value. Therefore, this function is considered a one-to-one function.

9- f(x) =log(base 2)x

  • The domain 0f this function is the set of all real numbers greater than 0.
  • The range of this function is the set of all real numbers
  • The one zero of this function is x=1.
  • Graphically, this function is symmetric to neither the y-axis nor the origin.
  • This function is considered neither odd nor even.
  • This function is not periodic.
  • For every f(x) value, there is only one x value. Therefore, this function is considered a one-to-one function.

10- f(x) = 1/x

  • The domain of this function is the set of all real numbers except for 0.
  • The range 0f this function is also the set of all real numbers except for 0.
  • There are no zeros for this function. Its graph never comes in contact with either axis.
  • Graphically, this function is symmetric to the origin.
  • Because it is symmetric to the origin, it is considered an odd function (f(-x)= -f(x)).
  • This function is not periodic.
  • This function is called a one-to-one function, meaning that for each f(x) value, only one x value exists.

11- f(x) - sqrt(x)

  • The domain of this function is the set of all real numbers greater than or equal to 0.
  • The range of this function is also the set of all real numbers greater than or equal to 0.
  • The one zero of this function is where x=0; (0,0).
  • Graphically, this function is symmetric to neither the y-axis nor the origin.
  • This function is considered neither even nor odd.
  • This function is not periodic.
  • This function is considered a one-to-one function, meaning that for every f(x) value, there is only one x value.

12- f(x) = sqrt(a^2-x^2)

  • The domain of this function is the set of all real numbers greater than or equal to -a, but less than or equal to +a.
  • The range of the function is the set of all real numbers greater than or equal to 0, but less than or equal to +a.
  • The zeros of the function are x=-a and x=a.
  • Graphically, this function is symmetric with respect to the y axis.
  • This function is considered an even function. f(-x)= f(x).
  • This function is not periodic.
  • This function is not considered to be a one-to-one function.

That's all for today

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