The function of the given graph is y = 5x⁵. The graph of a polynomial function shows the given behavior if the power is the odd value(n = 5).
What is the general form of a graph with a polynomial function?
The general form of a graph with a polynomial function is y = aₙxⁿ. Where 'n is odd'
If aₙ > 0; then the behavior of the graph on the left and right sides are given by [tex]\lim_{x \to -\infty} f(x) =-\infty[/tex] and [tex]\lim_{x \to \infty} f(x) =\infty[/tex] respectively.
If aₙ < 0; then the behavior of the graph on the left and right sides are given by [tex]\lim_{x \to -\infty} f(x) =\infty[/tex] and [tex]\lim_{x \to \infty} f(x) =-\infty[/tex] respectively.
Calculation:
From the given graph's behavior,
Left side: [tex]\lim_{x \to -\infty} f(x) =\infty[/tex] and
Right side: [tex]\lim_{x \to \infty} f(x) =-\infty[/tex]
So, the coefficient aₙ is aₙ < 0. So, it may be 4 and 5.
Since the power of the variable x is n is odd, the equation of the given graph is y = 5x⁵.
So, option 4 is correct.
Learn more about the graph of a polynomial function here:
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