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What is the range of f(x)=−3^x+4 ?


A-the set of real numbers less than 0


B- the set of real numbers less than 4


C- the set of real numbers greater than 4


D- the set of real numbers greater than 0


I have posted this three times, because I am not getting a explanataion and Im still confused as to why it would be B  if it even is. Please if someone could explain thank you .smiley

 Oct 22, 2018

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"

 Oct 22, 2018

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


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 \(\boxed B\)

 Oct 22, 2018

-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



cool cool cool

 Oct 22, 2018
edited by CPhill  Oct 22, 2018
edited by CPhill  Oct 22, 2018

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


 Oct 22, 2018

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

 Oct 29, 2018

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