Question

Use the drawing tool(s) to form the correct answer on the provided graph. The table below represents an exponential function, g, that has been vertically shifted from the parent function, f(x) = 2% х 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 parent function, f. Use the same x-values as used in the table for function g. Drawing Tools B Click on a tool to begin drawing. Undo Reset Seleci Point 8 rights reserved.

Answer 1

First let's define some points for the function f(x) = 2^x:

`\begin{gathered} x=0\to f(x)=1 \\ x=1\to f(x)=2 \\ x=2\to f(x)=4 \\ x=3\to f(x)=8 \\ x=4\to f(x)=16 \end{gathered}`

Comparing the values of g(x) with f(x) in the same values of x, we can see that the function g(x) is 12 units lesser than the function f(x).

So the size of the shift from function f(x) to g(x) is 12 units.

Half this shift is 6 units, so let's plot a new function, shifted only 6 units down from f(x):