Suppose g is a periodic function...

Question

suppose g is a periodic function. The period of g is 24, g(3)=67, and g(8)=70. Find each function value

 

a) g(27)

b) g(80)

c) g(-16)

d) g(51)

Answer 1

One of the properties of a periodic function is that it's values repeat after every period, both in the positive and negative directions on the number line.

In your case, since the period is 24, the values of the function g(x) will repeat after every x=24

Or, in algebraic notation, it can be written as:

g(24*n+x) = g(x)          eq1

  where n can be any integer, ... -2, -1, 0, 1, 2, ....

 

(a) g(27) can be written as g(24*1+3), which according to eq1 would be the same as g(3) = 67

 

(b) g(80) can be written as g(24*3+8), which according to eq would be _________________ (I'd let you fill the blanks!)

 

(c) g(-16) = g((24*(-1))+8) = ______________

 

(d) For g(51), I'd let you work on writing 51 as a multiple of 24 like above.