The function provided in the question is $f(x) = 2 \cdot x^5$. This is a polynomial function, not an exponential function, as it involves a power of $x$ rather than a constant base raised to a variable exponent.

Here's how we can determine the correct graph:

1. Since $f(x) = 2 \cdot x^5$, this function will exhibit the characteristics of an odd-power polynomial:

   • It will have a steep slope, rising to positive infinity as $x$ becomes large and positive.
   • It will fall to negative infinity as $x$ becomes large and negative.

2. The general shape of $x^5$ has an S-like curve, steepening faster than lower odd-power polynomials (like $x^3$), but still follows the general trend of odd polynomials.

From the options shown in the image:

• Graph B looks like the correct option because it shows an S-like curve, rising steeply in the positive $x$-direction and falling steeply in the negative $x$-direction, which aligns with the behavior of $f(x) = 2 \cdot x^5$.

So, the correct choice would be Option B.

Would you like further details on how to interpret the behavior of polynomial functions or other types of functions? Here are some related questions to deepen your understanding:

1. What are the differences in the shapes of graphs for even and odd power polynomials?
2. How does the coefficient affect the steepness of a polynomial function's graph?
3. What are some characteristics of exponential functions compared to polynomial functions?
4. How can you determine the end behavior of polynomial functions based on their degree?
5. What are the implications of a polynomial function having a positive or negative leading coefficient?

Tip: For any polynomial function, the degree of the polynomial (the highest power of $x$) determines the general shape and symmetry of the graph.