Question

The table below represents an exponential function, g, that has been vertically shifted from the parent function, f(x) = 2^x

. x 0 1 2 3 4
g(x) -11 -10 -8 -4 4 .
Determine the size of the shift from function fto function g. Then, plot the points of a function that is shifted only half as much as gfrom the parent function, f. Use the same x-values as used in the table for function g.​

Answer 1

Inputting the values of x into f(x):

`f(0)=2^0=1\\\\f(1)=2^1=2\\\\f(2)=2^2=4\\\\f(3)=2^3=8\\\\f(4)=2^4=16`

Comparing y-values of both functions:

f(x): 1, 2, 4, 8 , 16

g(x): -11, -10, -8, -4, 4

The difference between corresponding y-values of g(x) and f(x) is -12

Therefore, g(x) = f(x) - 12

If a new function h(x) is shifted by half as much, then h(x) = f(x) - 6

`h(0)=2^0-6=-5\\\\h(1)=2^1-6=-4\\\\h(2)=2^2-6=-2\\\\h(3)=2^3-6=2\\\\h(4)=2^4-6=10`