Question

How does the graph change between these two functions?

Answer 1

3 units left and 2 units up

Explanation:

The exponential function
`f(x) = 2^x` is the parent graph. All other exponential graphs with this base come from this graph. They are transformed by adding or subtracting to the input x or the output.

When values are added or subtracted with x, the function shifts left and right. Left is addition and right is subtraction.

When values are added or subtracted to the output of the function, the function shifts up and down. Addition is up and subtraction is down.

The function
`2^(x-1)+3` has x-1 which is 1 unit to the left from the parent graph. Adding 3 to the output, shifts the function up 3 from the parent graph.

The function
`2^(x+2)+5` has x+2 which is x-1+3 so is adding 3 and moves the function 3 units to the left. It also adds 5 instead of 3 so this moved the function 2 more units up.

From the second function to the first function, the graph shifts 3 units to the left and 2 units up.