Question

Let j(t)=4-t+2t^2. Find and simplify the expression below.
a. j(3t)
b. j(3-t)
c. 3j(t)
d. 3-j(t)

Answer 1

"Let j(t)=4-t+2t^2. Find and simplify the expression below. "

We'll focus on this part first. Ignore parts a,b,c,d for now.

Answer 2

j(t)=4-t+2t^2 is a function that takes one argument, t, and turns it into 4-t+2t^2

Answer 3

So, for each part, they want you to find how j(t) changes when you mess with the input. After you find that, they want you to simplify what you just found.

Answer 4

can you just help me figure out few of them

Answer 5

Ok, so for part a...

j(3t)

The argument is 3t. So before, everywhere you used to see t, there is now 3t.

Answer 6

We can analyze this term by term.

4-t+2t^2
...................................................................................................
The first term is +4. +4 doesn't depend on t, so we leave it alone.
........................................................................................................
The second term is -t. When you scale the input by 3, -t becomes -3t.
...........................................................................................................
The third term is +2t^2. When you scale the input by 3, this part becomes +2(3t)^2
Which is equal to:\[2(3^2t^2)\]Which is equal to 18t^2
.......................................................................................................


Add these together and you get:\[j(3t)=4 -3t +18t^2\]

Answer 7

ok can you do the b, c, and d one.. thanks

Answer 8

For (b), basically, everywhere you see t in the original function, replace it with (3-t)

Answer 9

For part (c), you're not changing the argument of the function, but rather multiplying the entire function by 3. The result should be:
\[3*j(t)=3*(4-t+2t^2)\]

Answer 10

Part (d) is 3-j(t).
You know j(t) is 4-t+2t^2
So 3-j(t) = 3-(4-t+2t^2)

Answer 11

I realize I explained this extremely poorly, but I'm sleep deprived. You might want to ask another question for additional clarity.

Answer 12

No, it's ok. I get it a little bit. Thanks for the help tho.