if F(x) is any function with period 5, determine the period of each related function.?

Question

1. y=F(x+1)
2. y=F(x)+5
3. y=F((1/2)x)
4. y=F(3x)

Answer 1

One thing to note is that the period is only affected by the number in front of the x. Therefore, a horizontal shift (such as in #1) or a vertical shift (such as #2) will NOT affect the peroid.

#3 on the other hand will stretch the function horizontally by a factor of 2. The formula to obtain the new period with the existing period is division; 5 divided by (1/2), which is the same as 5 x 2 = 10.

#4: Same deal. The period is 5/3.

Answer 2

1. 5
2. 5
3. 10
4. 5/3