Periodic functions in dilations

In summary, a periodic function is a mathematical function that repeats itself at regular intervals. A dilation is a transformation that changes the size of an object without changing its shape and can affect the period and amplitude of a periodic function. To graph a periodic function with a dilation, determine the period and dilation factor, plot points for one period, and use the dilation factor to stretch or shrink the points along the x-axis.
  • #1
zetafunction
391
0
is it possible to find a function f different from [tex] f(x)=constant [/tex]

with the property [tex] f(kx)=f(x) [/tex] for some real and positive 'k' ?

this is somehow 'dilation periodicity' is the equivalent to the periodic funciton [tex] f(x+k)=f(x) [/tex] for some positive 'k' for the traslation group
 
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  • #2
yes

try a substitution :wink:​
 

1. What is a periodic function?

A periodic function is a mathematical function that repeats itself in a predictable pattern at regular intervals. This means that as the input (x) increases, the output (y) will repeat the same values over and over again.

2. What is a dilation?

A dilation is a transformation that changes the size of an object without changing its shape. In the context of periodic functions, a dilation involves stretching or shrinking the function along the x-axis, resulting in a change in its period.

3. How do you determine the period of a periodic function?

The period of a periodic function is the distance between two consecutive points on the graph that have the same y-value. It can also be calculated by finding the difference between the x-coordinates of two consecutive points on the graph that have the same y-value.

4. Can dilations affect the amplitude of a periodic function?

Yes, dilations can affect the amplitude of a periodic function. If the dilation factor is greater than 1, the amplitude of the function will increase, and if it is less than 1, the amplitude will decrease.

5. How do you graph a periodic function with a dilation?

To graph a periodic function with a dilation, you first need to determine the period and the dilation factor. Then, plot the points for one period of the original function and use the dilation factor to stretch or shrink the points along the x-axis. Finally, repeat the pattern to graph the entire function.

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