Question

How do you graph `f( x ) = 352- 2\cdot 4^ { x }`?

Answer 1

`f(x)` is the standard exponential curve `y=4^x` scaled by `-2` and shifted `352` units positive ("up") on the `y-`axis.

Explanation:

`f(x) =352-2*4^x`

First consider the "parent" exponential graph of `y=4^x` below.

graph{4^x [-10, 10, -5, 5]}

Now, consider the graph above scaled by `-2` units below.

graph{-2*4^x [-10, 10, -5, 5]}

Finally, shift that graph `352` units up the `y-`axis as below.

graph{-2*4^x+352 [-6.324, 6.163, 346.966, 353.203]}

Hence, `f(x)` is the standard exponential curve `y=4^x` scaled by `-2` and shifted `352` units positive ("up") on the `y-`axis.