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avatar+712 

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
 #1
avatar+17332 
+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"

 Oct 22, 2018
 #2
avatar+624 
+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 \(\boxed B\)

.
 Oct 22, 2018
 #3
avatar+98196 
+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

 

 

cool cool cool

 Oct 22, 2018
edited by CPhill  Oct 22, 2018
edited by CPhill  Oct 22, 2018
 #4
avatar+17332 
+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
avatar+712 
0

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

 Oct 29, 2018

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