Question

# Graph each polynomial function. Factor first if the expression is not in factored form. f(x)=x^{2}(x+1)(x-1)

Polynomial graphs
Graph each polynomial function. Factor first if the expression is not in factored form.
$$\displaystyle{f{{\left({x}\right)}}}={x}^{{{2}}}{\left({x}+{1}\right)}{\left({x}-{1}\right)}$$

2021-01-23

$$\displaystyle{f{{\left({x}\right)}}}={x}^{{{2}}}{\left({x}+{1}\right)}{\left({x}-{1}\right)}$$ The function in factored form
The function has three zeros 0, -1, and 1
So, the graph of f(x) crosses the x-axis at (0,0), (-1,0), and (1,0)
To find the y-intercept, substitute 0 for x in f(x)
$$\displaystyle{f{{\left({x}\right)}}}={x}^{{{2}}}{\left({x}+{1}\right)}{\left({x}-{1}\right)}$$
$$\displaystyle{f{{\left({0}\right)}}}={\left({0}\right)}^{{{2}}}{\left({0}+{1}\right)}{\left({0}-{1}\right)}$$ Substitute 0 for x
$$\displaystyle={0}$$
So, the function f(x) crosses the y-axis at (0,0)
$$x^{2} \cdot x \cdot x=x^{4}$$
$$\displaystyle{x}\rightarrow\infty,{f{{\left({x}\right)}}}\rightarrow\infty$$
$$\displaystyle{x}\rightarrow-\infty,{f{{\left({x}\right)}}}\rightarrow\infty$$