Question

Question #34823

Answer 1

`f(x)=3^(x+9)+8`

Explanation:

In order to shift a graph upwards or downwards, we add or subtract the unit we want to shift it by.

To shift downwards, we subtract, and to shift upwards, we add.

For example, if we had a `g(x)`, and wanted to shift it `n` units upwards, we would do `g(x)+n`, and `n` units downwards would be `g(x)-n`.

In order to shift a graph to the left or the right, we add or subtract to our function (this won't seem clear now, read on.)

To shift to the left, we add, and to shift to the right, we subtract.

For example, if we had an `h(x)` and wanted to shift it `m` units to the left, we would do `h(x+m)`, and to shift `m` units to the right, we would do `h(x-m)`.

Using the above info, we can now say:

We have a `f(x)=3^x`. To shift to the left, we add `9` to `x`. We have to do `f(x+9)`, which is `3^(x+9)`. To shift upwards, we add, and so we do `f(x+9)+8`, which is `3^(x+9)+8`, our final function.

To prove above, we can graph both the functions:

`3^x` is:
graph{3^x [-18.02, 18.01, -9.01, 9.01]}

While `3^(x+9)+8` is:
graph{3^(x+9)+8 [-20.27, 20.26, -10.14, 10.13]}