"f A particular exponential function bas
the asymptote and doos not contain a
refiection across the x-axis. What is the range of this
function?

Question

"f A particular exponential function bas the asymptote $$ y=3 $$ and doos not contain a refiection across the x-axis. What is the range of this function?

UpStudy AI · Accepted Answer

1. Consider the general form of an exponential function:  
   $$
   f(x) = a \cdot b^x + c
   $$

2. The horizontal asymptote is given by $$ y = c $$. Since the asymptote is $$ y = 3 $$, we have:  
   $$
   c = 3
   $$

3. The condition that the function does not contain a reflection across the x-axis implies that the coefficient $$ a $$ is positive, so $$ a > 0 $$.

4. With $$ a > 0 $$, the function behaves in the standard exponential manner. As $$ x \to -\infty $$, the term $$ b^x $$ approaches 0, and the function approaches $$ y = 3 $$ (but never reaches 3). As $$ x \to \infty $$, $$ b^x $$ grows, and thus $$ f(x) $$ increases without bound.

5. Therefore, the range of the function is:  
   $$
   (3, \infty)
   $$
The range of the function is all real numbers greater than 3.

"f A particular exponential function bas
the asymptote and doos not contain a
refiection across the x-axis. What is the range of this
function?

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"f A particular exponential function bas the asymptote and doos not contain a refiection across the x-axis. What is the range of this function?

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"f A particular exponential function bas
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