Question

~~~PLEASE MEDAL @jim_thompson5910 for helping me!!!~~~

George goes out for a run. The graph shows the function g(t) which gives his distance traveled in miles, t minutes after he starts running. The graphs of f(t) and h(t) represent the distances his friends, Francine and Hector, have traveled t minutes after George started running.

Francine (red): f(t)=1/10t+1
George (blue): g(t)=1/10t
Hector (green): h(t)=1/10(t-15)

1. Write the rule for the function g(t). Then write rules for f(t) and h(t) in terms of g(t).

Answer 1

That is my graph, the names of the colors next to the lines are which lines they are.

Answer 2

@jim_thompson5910 please help, we did not go over this vocab in class

Answer 3

I don't understand the question fully. They gave you the graphs and the functions already. I'm not sure what they're asking.

Answer 4

Me neither... that's why I brought it up here, I was hoping someone else could have gone through this before.

Answer 5

The instructions say

`1. Write the rule for the function g(t). Then write rules for f(t) and h(t) in terms of g(t).`

But the first part is already given. They gave you g(t)=1/10t

And so is the second part since they gave you f(t)=1/10t+1 and h(t)=1/10(t-15)

Answer 6

oh wait, nvm I re-read things and I see what they want now

Answer 7

`Then write rules for f(t) and h(t) in terms of g(t).`

so what they want is that you write f(t) to have g(t) somewhere in the expression on the right side

example:

f(t) = 2*g(t)+5

Answer 8

Oh, thank you so much!!!

Answer 9

No one else got this problem, lol. You will get a follow for this!

Answer 10

what would f(t) be equal to, in terms of g(t) ?

Answer 11

I dont know...

Answer 12

oh f(t)= g(t) +1

Answer 13

yes you shift the blue function (g(t)) up 1 unit

Answer 14

and h(t) = g(t) -15/10

Answer 15

ah, this makes so much more sense!

Answer 16

Oh kind soul, what would I do without you? =D

Answer 17

or you can think of it like this

\[\Large g(t) = \frac{1}{10}t\]
\[\Large \color{red}{g(t)} = \color{red}{\frac{1}{10}t}\]
--------------------------------------------------
\[\Large f(t) = \frac{1}{10}t + 1\]
\[\Large f(t) = \color{red}{\frac{1}{10}t} + 1\]
\[\Large f(t) = \color{red}{g(t)} + 1\]
\[\Large f(t) = g(t) + 1\]

Answer 18

yeah.

Answer 19

\[\Large g(t) = \frac{1}{10}t\]
\[\Large \color{red}{g(t)} = \color{red}{\frac{1}{10}t}\]
--------------------------------------------
\[\Large h(t) = \frac{1}{10}(t-15)\]
\[\Large h(t) = \frac{1}{10}t+\frac{1}{10}*(-15)\]
\[\Large h(t) = \frac{1}{10}t-\frac{15}{10}\]
\[\Large h(t) = \frac{1}{10}t-\frac{3}{2}\]
\[\Large h(t) = \color{red}{\frac{1}{10}t}-\frac{3}{2}\]
\[\Large h(t) = \color{red}{g(t)}-\frac{3}{2}\]
\[\Large h(t) = g(t)-\frac{3}{2}\]
or
\[\Large h(t) = g(t)-1.5\]

Answer 20

f(t) is a vertical translation up 1
h(t) is a horizontal translation left 1.5

Answer 21

`f(t) is a vertical translation up 1` agree

`h(t) is a horizontal translation left 1.5` disagree

Answer 22

hint: look at the x intercepts of the blue and green functions