CAN SOMEONE PLEASE HELP ME!!
Consider the polynomial function h(x) = -7x6 + 3x4 – 5x2.
What is the end behavior of the graph of h ?

Answer: As x -> ♾, h(x) -> -♾, and as x -> -♾,h(x) -> -♾

Step-by-step explanation:

The end behavior is x ----> ∞ then h(x) ----> -∞, and when x ----> -∞ then h(x) -----> -∞.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

h(x) = -7[tex]x^6[/tex] + 3 [tex]x^4[/tex]– 5x².

If we plot the Equation on the Graph we can see a parabolic Curve.

This Curve tells as x tends to ∞ the value of h(x) tends to -∞.

and, when x tends to -∞ the value of h(x) tends to -∞.

Hence, the end behavior is x ----> ∞ then h(x) ----> -∞.

and, when x ----> -∞ then h(x) -----> -∞.

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