$\newenvironment {prompt}{}{} \newcommand {\ungraded }[0]{} \newcommand {\text }[1]{#1} \newcommand {\sagecheck }[2]{ \ifthenelse {}{}{}\textit {} } \newcommand {\HyperFirstAtBeginDocument }[0]{\AtBeginDocument }$
1 : Consider the functions $f(x) = \sage {p1f1}$ and $g(x) = \sage {p1f2}$. Compute the following:
• $\left (f+g\right )(x) = \answer {\sage {p1ans1}}$
• $\left (f-g\right )(x) = \answer {\sage {p1ans2}}$
• $\left (fg\right )(x) = \answer {\sage {p1ans3}}$
• $\left (\frac {f}{g}\right )(x) = \answer {\sage {p1ans4}}$
2 : Consider the functions $f(x) = \sage {p2f1}$ and $g(x) = \sage {p2f2}$. Compute the following:
• $\left (f+g\right )(x) = \answer {\sage {p2ans1}}$
• $\left (f-g\right )(x) = \answer {\sage {p2ans2}}$
• $\left (fg\right )(x) = \answer {\sage {p2ans3}}$
• $\left (\frac {f}{g}\right )(x) = \answer {\sage {p2ans4}}$
3 : Consider the functions $f(x) = \sage {p3f1}$ and $g(x) = \sage {p3f2}$. Compute the following:
• $\left (f+g\right )(x) = \answer {\sage {p3ans1}}$
• $\left (f-g\right )(x) = \answer {\sage {p3ans2}}$
• $\left (fg\right )(x) = \answer {\sage {p3ans3}}$
• $\left (\frac {f}{g}\right )(x) = \answer {\sage {p3ans4}}$
4 : Consider the functions $f(x) = \sage {p4f1}$ and $g(x) = \sage {p4f2}$. Compute the following:
• $\left (f+g\right )(x) = \answer {\sage {p4ans1}}$
• $\left (f-g\right )(x) = \answer {\sage {p4ans2}}$
• $\left (fg\right )(x) = \answer {\sage {p4ans3}}$
• $\left (\frac {f}{g}\right )(x) = \answer {\sage {p4ans4}}$