What is the range of f(x)=−3^x+4 ?

At large -x values the -3^x   nears zero and the expression is equal to ~4

as x approaches 0 the -3^x becomes  -1    and the expression becomes 3

as x goes positive  -3^x becomes a large negative number dwarfing the '4' in the expression and the entire expression becomes more and more negative

So it has a maximum of ALMOST 4   and is less than that or negative everywhere else......

Answer "B"

\(\mathrm{Range\:of\:}-3^x+4:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)<4\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:4\right)\end{bmatrix}\)

The range of an exponential function of the form \(-c \cdot n^{ax+b} + k\) is \(f(x) < k\)

Therefore, \(k = 4\).

So, the solution is \(f(x) < 4\) which would give us answer choice \(\boxed B\)

-3^x   +  4

"Range" refers to the y values covered by the function

Note that when x is a large negative, the function reaches its highest point  ≈  4

As  x appoaches 0, the function approaches  3

As x gets more and more positive, the finction gets more and more negative

So..... "B"  is correct

Look at the graph  here to confirm  this for yourself  :   https://www.desmos.com/calculator/pw6f0aztxl

I tried posting a graph earlier, but the whole 'waiting for moderator' thingie is whacko today and nothing is getting approved

Thank you so much guys for all your explanations it was B.