MATH SOLVE

4 months ago

Q:
# 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.

Accepted Solution

A:

Answer:Option 2 is correct[tex]g(x) = (\frac{1}{2})5^{(x+3)}+2[/tex]Step-by-step explanation:We can se ethat the given function is an exponential function.The function is:5^xIn order to compress the function the original function is multiplied a constant.As the function is compressed by a factor of 1/2The function will become:g(x) = 1/2 * 5^xNow 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:[tex]g(x) = \frac{1}{2}5^{x+3}[/tex]Then the function is shifted upwards two units, the vertical shhift is added to the whole function so the function will become:[tex]g(x) = (\frac{1}{2})5^{(x+3)}+2[/tex]Hence, Option 2 is correct ..