Question

The parent function f(x)=5^x has been virtually compressed by a factor of 1/2, shifted to the left three units and up two units. Chose the correct function to represent the transformation.

Answer 1

Option 2 is correct

`g(x) = ((1)/(2))5^((x+3))+2`

Explanation:

We can se ethat the given function is an exponential function.

The function is:

5^x

In order to compress the function the original function is multiplied a constant.

As the function is compressed by a factor of 1/2

The function will become:

g(x) = 1/2 * 5^x

Now the function is shifted to left which is a horizontal shift. For horizontal shift of n units, n is added to the power so the function will become:

`g(x) = (1)/(2)5^(x+3)`

Then the function is shifted upwards two units, the vertical shhift is added to the whole function so the function will become:

`g(x) = ((1)/(2))5^((x+3))+2`

Hence, Option 2 is correct ..