SOLUTION: Determine the domain, range, equation of the horizontal asymptote and construct the graph of the following exponential function: f(x) =6^3-x - 4

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Determine the domain, range, equation of the horizontal asymptote and construct the graph of the following exponential function: f(x) =6^3-x - 4      Log On


   

Question 1195058: Determine the domain, range, equation of the horizontal asymptote and construct the graph of the following exponential function: f(x) =6^3-x - 4
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29+=6%5E3-x+-+4++++
I guess you hae 6x%5E3
f%28x%29+=6x%5E3-x+-+4+
domain: R (all real numbers)
range: R (all real numbers)
equation of the horizontal asymptote: no horizontal asymptotes found

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+6x%5E3-x+-+4%29+


Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The function you show is not an exponential function:

f(x) = 6^3-x-4 --> f%28x%29+=+6%5E3-x-4

If you are working on a problem like this, your math knowledge should be enough to know that proper use of parentheses is important.

Since you said the function is exponential, undoubtedly the function you intended to show is this:

f(x) = 6^(3-x)-4 --> f%28x%29+=+6%5E%283-x%29-4

domain: all real numbers. There is no restriction on the input value in any exponential equation.

range and horizontal asymptote: The range is (-4,infinity). Without the "-4", the exponential function value is always positive but gets as close to 0 as you want. So with the "-4" the horizontal asymptote is y=-4.

a graph, showing the horizontal asymptote:

graph%28400%2C400%2C-1%2C6%2C-10%2C10%2C6%5E%283-x%29-4%2C-4%29