Question

Can anyone help me? Which function is graphed on the right?

Y=2^x+3-2
Y=2^x-3+2
Y=2^x-2+3
Y=2^x-2-3

Answer 1

The answer is C

Explanation:

Answer 2

`y=2^(\left(x-2\right))+3`

Explanation:

To solve this problem, we need to start with the parent function of the exponential function, which is
`f(x)=a^x`, where
`a` is the base. In our problem,
`a=2`, so our parent function here is
`y=2^x`. Then, we need to perform some transformations to our parent function. Thus:

1. Vertical shrink:

A vertical shrink is a nonrigid transformation because the graph of the function get a distortion in the shape, so this transformation is as follows:

`g(x)=cf(x)`

where
`c` in this problem equals 0.25 because:

`y=0.25(2^x) \\ \\ y=(1)/(4)(2^x) \\ \\ y=(2^x)/(2^2) \\ \\ y=2^((x-2))`

2. Vertical shift:

The graph of the function
`y=2^((x-2))` get a vertical shift given by:

`y=2^((x-2))+3`

So the graph is shifted 3 units up. So the result is the graph shown above.