Five Basic Functions

Learning Enhancement Team
Factsheet:
Sine
Five Basic Functions
Periodic function of an angle x
Written Inverse Derivative
sin x
sin1 x
cos x
Integral
Domain
Range
Comments
 cos x  c
Real Numbers
 1  sinx   1
Odd function
sin x    sinx 
f (x)
Period is 2
sinx   / 2  cosx 
sin0  0
x
sin / 2  1
sin   0
sin3 / 2  1
sin2   0
sinn   0
Cosine
Periodic function of an angle x
Written
Inverse
Derivative Integral
Domain
Range
cos x
cos 1 x
 sin x
Real Numbers
 1  cosx   1
sin x  c
Comments
Even function
cos x   cosx 
Period is 2
cosx   / 2  sinx 
f (x)
cos0  1
cos / 2  0
x
cos   1
cos3 / 2  0
cos2   1
cos / 2  n   0
Exponential
Written
ex
or
expx 
The exponential function of x
Pronounced Inverse Derivative Integral
“e to the x”
ex
ln x
ex  c
Domain
Range
Real
Numbers
ex  0
Comments
e0  1
e1  e
f (x)
x
Logarithm
Written
ln x
The natural logarithm of x
Pronounced Inverse Derivative
“el en of x”
or
“lun x”
ex
1
x
Integral
x ln x  x  c
Domain
Range
x 0
Real
Numbers
Comments
ln1  0
ln e  1
ln x  log e x
f (x)
x
Power functions x n
n2
Quadratic function
Written
x2
Inverse
x
Derivative
2x
Integral
x3
c
3
Domain
Real Numbers
Range
x2  0
f (x)
Comments Turning point at 0 , 0
n  2
Written
x
Inverse square
function
1
x2
f (x)
1
Inverse
x
Derivative
 2x 3
Integral

1
c
x
Real Numbers,
x0
1
0
Range
x2
Asymptotes at
Comments x  0 and y  0
Domain
n3
Cubic function
Written
x3
Inverse
3
Derivative
3x 2
Integral
x4
c
4
Domain
Real Numbers
Range
Real Numbers
x
f (x)
x
Point of Inflection
Comments at 0 , 0
x
n  1
Reciprocal Function
Written
1
x
Inverse
1
x
Derivative
 x 2
Integral
ln x  c
Domain
Real Numbers, x  0
Range
Real Numbers, x  0
Comments
Asymptotes at
x  0 and y  0
Self-inverse
f (x)
x
Want to know more?
If you have any further questions about this topic you can make an appointment to see a
Learning Enhancement Tutor in the Student Support Service, as well as speaking to
your lecturer or adviser.



Call:
Ask:
Click:
01603 592761
ask.let@uea.ac.uk
https://portal.uea.ac.uk/student-support-service/learning-enhancement
There are many other resources to help you with your studies on our website.
For this topic, there is a webcast.
Your comments or suggestions about our resources are very welcome.
Scan the QR-code with a
smartphone app for a
webcast of this factsheet.

Download Report