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

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)`

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)=(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.