Question

Given that f(x) and g(x) are linear functions and f(3) = 4 and f(2)=6. g(1) =3 and g(-1)=2 (Hint: These are coordinate points!) f) and g(x) are because their (3 points total) #10 9. ** 10. ** parallel slopes The same (B) Reciprocals perpendicular neither parallel nor perpendicular y-intercepts equations (c Opposite reciprocals

Answer 1

`\begin{gathered} \text{First of all, we wil find the equations of f and g. Since f is linear, it's slope is:} \\ m=\frac{f(3)-f(2)_{}}{3-2} \\ =(4-6)/(1) \\ m=-2 \\ \\ \text{thus, f(x)=-2x+b} \\ \text{now, } \\ f(3)=4, \\ -2(3)+b=4 \\ b=4+6 \\ b=10 \\ \\ f(x)=-2x+10 \\ \\ \\ \text{now we will find g(x)} \end{gathered}`
`\begin{gathered} m=(g(1)-g(-1))/(1-(-1)) \\ m=(3-2)/(2) \\ m=(1)/(2) \\ g(x)=(1)/(2)x+b \\ g(1)=3 \\ (1)/(2)+b=3 \\ b=3-(1)/(2) \\ b=(5)/(2) \\ \\ \text{ thus} \\ g(x)=(1)/(2)x+(5)/(2) \end{gathered}`
`\begin{gathered} \text{ Now, since the slopes are not equal, the functions are not parallel.} \\ \text{But, they are opposite reciprocals! because} \\ (-2)((1)/(2))=-1 \\ \text{ thus the functions are perpendicular} \end{gathered}`

f(x) and g(x) are perpendicular because their slopes are opposite reciprocals!