Question

1. A train travels along a straight track so that its distance in miles, d(t), from Newark Penn Station is given as a function of time, t minutes. If after 2 minutes the train has traveled 6 miles, and after 5 minutes the train has traveled 12 miles, the average rate (think slope!) that the train travels is 2 with a unit of miles/ minute

Answer 1

Start by finding the functions f(x) and g(x)

for f(x)

slope

`\begin{gathered} m=((1-(-1)))/((0-1)) \\ m=-2 \end{gathered}`

y intercept= 1

full equation will be

`f(x)=-2x+1`

find g(x)

slope

`\begin{gathered} m=(3-(-3))/(1-0) \\ m=6 \end{gathered}`

y intercept= -3

full equation will be

`g(x)=6x-3`

multiply the functions

`\begin{gathered} (6x-3)\cdot(-2x+1) \\ -12x^2+6x+6x-3 \\ h(x)=-12x^2+12x-3 \end{gathered}`

the y-intercept will be -3