Question

You are given the exponential function g(x) = 4–x. Which option below gives the formula for a new function h created by shrinking g by a factor of 2 along the y-axis? h(x) = 4–x–1 h(x) = 2(4–x) h(x) = 0.5(4–x) h(x) = 4–x+1

Answer 1

I don't understand, g(x) = 4 - x  is not an exponential function. Did you miss any thing?

Answer 2

Answer:

The option which gives the formula for a new function h created by shrinking g by a factor of 2 along the y-axis is:

             $h(x)=0.5\cdot 4^{-x}$

Step-by-step explanation:

We are given a parent function which is a exponential function as:

            $g(x)=4^{-x}$

and the shrinking of a function along the y-axis means that there is a vertical shrink.

Now, it is given that the function g is vertically compressed by a factor of 2.

This means that the transformed function is given by:

   $h(x)=\dfrac{1}{2}g(x)\\\\\\i.e.\\\\\\h(x)=0.5\cdot 4^{-x}$

Also, by the graph we could observe that at x=0 the value of x is compressed when the function was divided by 2.