Given the following function:
[tex]h(x)=0.1(x-3)^2(x+3)^3[/tex]
The function has a degree = 5 (odd number)
And the leading coefficient = 0.1 (A positive number)
So, the end behavior will be as follows:
[tex]\begin{gathered} x\to\infty\Rightarrow h(x)\to\infty \\ x\to-\infty\operatorname{\Rightarrow}h(x)\to-\infty \end{gathered}[/tex]
So, the answer will be:
The end behavior of the function is down to the left
and up to the right.
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Part 2: Find the y-intercepts
The y-intercept is the value of y when x = 0
so, we will substitute x = 0 and find the value of y
[tex]y=0.1(0-3)^2(0+3)^3=0.1*9*27=24.3[/tex]
So, the answer will be:
y-intercept = 24.3
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Now, we'll graph the function using the data from the previous parts
We will make a table between x and y to graph the function
The table and the graph will be as follows:
