Question

The graph of two functions, f and g, is illustrated below. Use the graph to answer parts (a) through (f).

Answer 1

$\begin{gathered} a) \\ \mleft(f+g\mright)\mleft(2\mright)=f\mleft(2\mright)+g\mleft(2\mright) \\ from\text{ the graph} \\ f(2)=4 \\ g(2)=-2 \\ (f+g)(2)=4+(-2) \\ (f+g)(2)=4-2 \\ (f+g)(2)=2 \\ b) \\ \text{f+g)(4)} \\ \mleft(f+g\mright)\mleft(4\mright)=f\mleft(4\mright)+g\mleft(4\mright) \\ from\text{ the graph} \\ f(4)=2 \\ g(4)=-6 \\ (f+g)(4)=2+(-6) \\ (f+g)(4)=2-6 \\ (f+g)(4)=-4 \\ c) \\ (f-g)(6)=f(6)-g(6) \\ \text{from the graph} \\ f(6)=0 \\ g(6)=-2 \\ (f-g)(6)=0-(-2) \\ (f-g)(6)=0+2 \\ (f-g)(6)=2 \\ d) \\ (g-f)(6)=g(6)-f(6) \\ \text{from the graph} \\ f(6)=0 \\ g(6)=-2 \\ (g-f)(6)=-2-0 \\ (g-f)(6)=-2 \\ e) \\ (f\cdot g)(2)=f(2)\cdot g(2) \\ from\text{ the graph} \\ f(2)=4 \\ g(2)=-2 \\ (f\cdot g)(2)=(4)\cdot(-2) \\ (f\cdot g)(2)=-8 \\ f) \\ (\frac{f}{g})(4)=\frac{f(4)}{g(4)} \\ from\text{ the graph} \\ f(4)=2 \\ g(4)=-6 \\ (\frac{f}{g})(4)=\frac{2}{-6}=-\frac{1}{3} \\ (\frac{f}{g})(4)=-\frac{1}{3} \end{gathered}$