Question

Polynomial function: (a) List each real zero and its multiplicity. (b) Determine whether the graph crosses or touches the $x$ -axis at each $x$ -intercept. (c) Determine the maximum number of turning points on the graph. (d) Determine the end behavior; that is, find the power function that the graph of f resembles for large values of $|x|$. $$ f(x)=\frac{1}{2}\left(2 x^{2}+9\right)^{2}\left(x^{2}+7\right) $$

          Polynomial function:
(a) List each real zero and its multiplicity.
(b) Determine whether the graph crosses or touches the $x$ -axis at each $x$ -intercept.
(c) Determine the maximum number of turning points on the graph.
(d) Determine the end behavior; that is, find the power function that the graph of f resembles for large values of $|x|$.
$$
f(x)=\frac{1}{2}\left(2 x^{2}+9\right)^{2}\left(x^{2}+7\right)
$$

Added by Alexander W.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Suman Saurav Thakur

Step 1

(a) To find the real zeros, we need to set the function equal to zero and solve for $x$: $$ \frac{1}{2}(2x^2 + 9)^2(x^2 + 7) = 0 $$ Since the first term $(2x^2 + 9)^2$ is squared, it will always be positive, and there are no real zeros that will make this term Show more…

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Polynomial function: (a) List each real zero and its multiplicity. (b) Determine whether the graph crosses or touches the $x$ -axis at each $x$ -intercept. (c) Determine the maximum number of turning points on the graph. (d) Determine the end behavior; that is, find the power function that the graph of f resembles for large values of $|x|$. $$ f(x)=\frac{1}{2}\left(2 x^{2}+9\right)^{2}\left(x^{2}+7\right) $$