Using limits, it is found that the polynomial that represents the function described is:
- [tex]-2x^7 + \frac{1}{2}x^6 - 8x^5 + 3x^4 + 2x^3 - 5x^2 + x - 7[/tex]
Limits:
- The end behavior of the graph of a function f(x) is given by the limit of the function f(x) as x goes to infinity.
In this problem:
- The left side is rising, hence [tex]\lim_{x \rightarrow -\infty} f(x) = \infty[/tex], that is, the leading coefficient is negative and the highest degree exponent is off.
- The right side is falling, hence [tex]\lim_{x \rightarrow \infty} f(x) = -\infty[/tex], which also checks the above bullet point.
Hence, the polynomial is:
[tex]-2x^7 + \frac{1}{2}x^6 - 8x^5 + 3x^4 + 2x^3 - 5x^2 + x - 7[/tex]
To learn more about limits, you can take a look at https://brainly.com/question/22026723
