Answer:
See below.
Step-by-step explanation:
The value of the highest degree ( x^9) is 9 - odd.
So this well rise from negative infinity on the left and rise to positive infinity on the right - or, putting it in a different way, fall to the left and rise to the right.
Answer:
The end behavior is to grow
Step-by-step explanation:
The first step is to identify the zeros of the function, it means, the values of x at which the function becomes zero. For achieving that, it necessary to factorize.
[tex]f(x)=10x^9-4x[/tex]
[tex]f(x)=x(10x^8-4)[/tex]
According to the previous, the zeros are:
If we replace those values in [tex]f(x)[/tex], we obtain:
Now, imagine the following two situations:
[tex]f(-\infty )=-\infty (10\cdot (-\infty )^8-4)[/tex]
The term [tex](-\infty )^8/[tex] equals [tex]\infty [/tex] because the sign (-) is also raised to the power 8. The equation would be:
[tex]f(-\infty )=-\infty (10\cdot (\infty )-4)[/tex]
If you multiply [tex]\infty[/tex] by 10 and subtract 4, the result is still [tex]\infty[/tex]. The equation would be:
[tex]f(-\infty )=-\infty \cdot (\infty )[/tex]
The only important thing in the previous expression is the multiplication of the signs, it means, a plus and a minus make a minus. So, [tex]f(-\infty )=-\infty[/tex], it means, THE GRAPH TENDS TO DECREASE WHEN X TENDS TO NEGATIVE INFINITIVE
[tex]f(\infty )=\infty (10\cdot (\infty )^8-4)[/tex]
If you multiply [tex]\infty[/tex] by 10 and subtract 4, the result is still [tex]\infty[/tex]. The equation would be:
[tex]f(\infty )=\infty \cdot (\infty )[/tex]
The only important thing in the previous expression is the multiplication of the signs, it means, two pluses make a plus. So, [tex]f(\infty )=\infty[/tex], it means, THE GRAPH TENDS TO GROW WHEN X TENDS TO POSITIVE INFINITIVE
Thus, if you start giving arbitrary values to x, greater than [tex](4/10)^{1/8}=0.8917[/tex], the value of [tex]f(x)[/tex] becomes greater. It means that the end behavior of the graph is to grow.
Please find attached the graph of the equation
