Question

Which function could be a stretch of the exponential decay function shown on the graph? f(x) = 2(6)x f(x) = 1/2(6)x f(x) = 2(1/6) f(x) =1/2(1/6)

Answer 1

The correct option is, i.e.,
`f(x)=2((1)/(6))^x`.

Explanation:

The exponential function is defined as

`f(x)=ab^x`

Where, a represents the vertical stretch and compression and b is the growth factor.

If |a|>1, then it represents vertical stretch and if |a|<1, then it represents vertical compression.

If b>1, then the function is a growth function and If 0<b<1, then the function is a decay function.

Since we have to find the function that is a stretch of the exponential decay function, therefore the value of a>1 and value of b<1.

In option 1, a>1 and value of b>1. So, option 1 is incorrect.

In option 2, a<1 and value of b>1. So, option 2 is incorrect.

In option 3, a>1 and value of b<1. So, option 3 is correct.

In option 4, a<1 and value of b<1. So, option 4 is incorrect.