Solution Bank Polynomials Target E
Answers to the Practice Problems are below in random order.
\(\begin{align}&\text{Odd}\ & \ \ \ \ &\text{Odd}\ & \ \ \ \ &\text{Odd}\ & \ \ \ \ &\text{Odd}\\\\
&x=6,\:-2\pm i\sqrt{5}\ & \ \ \ \ &\text{Even}\ & \ \ \ \ &\text{Even}\ & \ \ \ \ &\text{Even}\\\\
&\text{Neither}\ & \ \ \ \ &\text{Neither}\ & \ \ \ \ &\text{Neither}\ & \ \ \ \ &9x^{28}\end{align}\)
\(\text{The coefficient of a term does not affect if the function is even or odd.}\\ \text{Since all the terms have even exponents, g(-x)=g(x), so the function is even.}\)
\((3x^2-8)(3x^2+8);\ \ \ \ (x^2-5)(x+2)(x-2);\ \ \ \ (2x-3)(4x^2+6x+9);\ \ \ \ (3x+4)(x+3)(x-3)\)
\(\text{Odd function}; \text{Degree:}\ 5, LC: -1; \text{As}\ x\ \longrightarrow\ -\infty,\ f(x)\ \longrightarrow\ +\infty,\ \text{as}\ x\ \longrightarrow\ +\infty,\ f(x)\ \longrightarrow\ -\infty;\\ \text{Domain:}\ (-\infty,\infty)\ \text{Range:} (-\infty,\infty)\)
\(\text{Even; Degree}\ 4, LC:\ 3\ \text{As}\ x\ \longrightarrow\ -\infty,\ f(x)\ \longrightarrow\ +\infty,\ \text{as}\ x\ \longrightarrow\ +\infty,\ f(x)\ \longrightarrow\ +\infty;\ \text{Domain:}\ (-\infty,\infty)\ \text{Range:}\ [-4,\infty)\)
\(\text{Odd degree functions have an end behavior such as “As}\ x\ \longrightarrow\ -\infty,\ f(x)\ \longrightarrow\ - \infty,\ \text{as}\ x\ \longrightarrow\ +\infty,\ f(x)\ \longrightarrow\ +\infty”.\\\text{These graphs cannot have a reflection symmetry in the y-axis as even functions do.}\)
Answers to the Practice Problems are below in random order.
\(\begin{align}&\text{Odd}\ & \ \ \ \ &\text{Odd}\ & \ \ \ \ &\text{Odd}\ & \ \ \ \ &\text{Odd}\\\\
&x=6,\:-2\pm i\sqrt{5}\ & \ \ \ \ &\text{Even}\ & \ \ \ \ &\text{Even}\ & \ \ \ \ &\text{Even}\\\\
&\text{Neither}\ & \ \ \ \ &\text{Neither}\ & \ \ \ \ &\text{Neither}\ & \ \ \ \ &9x^{28}\end{align}\)
\(\text{The coefficient of a term does not affect if the function is even or odd.}\\ \text{Since all the terms have even exponents, g(-x)=g(x), so the function is even.}\)
\((3x^2-8)(3x^2+8);\ \ \ \ (x^2-5)(x+2)(x-2);\ \ \ \ (2x-3)(4x^2+6x+9);\ \ \ \ (3x+4)(x+3)(x-3)\)
\(\text{Odd function}; \text{Degree:}\ 5, LC: -1; \text{As}\ x\ \longrightarrow\ -\infty,\ f(x)\ \longrightarrow\ +\infty,\ \text{as}\ x\ \longrightarrow\ +\infty,\ f(x)\ \longrightarrow\ -\infty;\\ \text{Domain:}\ (-\infty,\infty)\ \text{Range:} (-\infty,\infty)\)
\(\text{Even; Degree}\ 4, LC:\ 3\ \text{As}\ x\ \longrightarrow\ -\infty,\ f(x)\ \longrightarrow\ +\infty,\ \text{as}\ x\ \longrightarrow\ +\infty,\ f(x)\ \longrightarrow\ +\infty;\ \text{Domain:}\ (-\infty,\infty)\ \text{Range:}\ [-4,\infty)\)
\(\text{Odd degree functions have an end behavior such as “As}\ x\ \longrightarrow\ -\infty,\ f(x)\ \longrightarrow\ - \infty,\ \text{as}\ x\ \longrightarrow\ +\infty,\ f(x)\ \longrightarrow\ +\infty”.\\\text{These graphs cannot have a reflection symmetry in the y-axis as even functions do.}\)
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