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# What is the range of f(x)=−3^x+4 ?

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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 .

Oct 22, 2018

#1
+18274
+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......

Oct 22, 2018
#2
+625
+11

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

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 $$\boxed B$$

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Oct 22, 2018
#3
+101084
+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

Oct 22, 2018
edited by CPhill  Oct 22, 2018
edited by CPhill  Oct 22, 2018
#4
+18274
+3

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

Oct 22, 2018
#5
+922
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Thank you so much guys for all your explanations it was B.

Oct 29, 2018