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 .

jjennylove
Oct 22, 2018

#1**+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"

ElectricPavlov
Oct 22, 2018

#2**+9 **

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

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 \(\boxed B\)

KnockOut
Oct 22, 2018

#3**+3 **

-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

CPhill
Oct 22, 2018

#4**+3 **

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

ElectricPavlov
Oct 22, 2018