Robert was able to understand that in a function

*f*(

*x*) =

*b^x*, regardless of the base

*b*, when

*x*is 0, the function has a value of 1. This is because any base raised to an exponent of 0 is equal to 1.

I asked Robert to consider how the y-intercept would change if the function

*b^x*times a constant

*a*. First I gave him an example of

*f(x) =*2 *

*b^x.*He told me that the y-intercept is (0, 2). I then asked him to extend this idea to any constant

*a*. He was able to see that the y-intercept would be (0, a).

I then asked Robert to consider the range of a function

*f*(

*x*) =

*b^x.*He was able to see that the function will never reach 0, or be less than 0. I then asked him to consider what would happen if he added five on the end, as in the function

*g*(

*x*) =

*b^x +*5

*.*After the previous question, Robert quickly concluded that the range of the function is all numbers greater than 5.

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