The graph of the function $$ f(x)=3^{x} $$ lies in which quadrant(s)? 1) I, only 2) I and II 3) I and III 4) I and IV

Question

UpStudy AI · Accepted Answer

1. The function is given as $$ f(x)=3^{x} $$.

2. The **domain** of $$ f(x) $$ is all real numbers, i.e., $$ x \in (-\infty, \infty) $$.

3. The **range** is $$ (0, \infty) $$ since $$ 3^{x} $$ is always positive for any real $$ x $$.

4. For $$ x>0 $$ (first quadrant), the corresponding $$ y $$-values are positive.

5. For $$ x<0 $$ (second quadrant), the corresponding $$ y $$-values are still positive.

6. Hence, the graph is located in both the first and second quadrants.

The correct answer is: 2) I and II.
The graph of $$ f(x)=3^{x} $$ is in the first and second quadrants.

The graph of the function lies in which quadrant(s)?

I, only

I and II

I and III

I and IV