Find Domain & Sketch Graph: Calculus Functions

[Corkery]

Homework Statement

Find the Domain and sketch the graph of the function if a grid is provided.

1. p(t) = | 2t + 3 |

Homework Equations

The Attempt at a Solution

Well basically in the book it said that it would end up looking something like this... {2t + 3 for (2t + 3) > 0 (<----- that is suppost to be greater or equal to)

and the other part was suppost to be { -(2t + 3) for (2t + 3) < 0


to me this makes no sense of why this is suppost to end up this way. Also ignore the part that said if you're provided a grid. You don't have to solve it or anything like that, but just explain this to me. Thank you, Corkery.

 

[Mindscrape]

Since the absolute value does not allow for negatives, the function must be split into the piecewise function of the part where it is negative, and the part where it is positive.

 

[Corkery]

Since the absolute value does not allow for negatives, the function must be split into the piecewise function of the part where it is negative, and the part where it is positive.

why is one of the equations greater than or equal to zero and another is less then zero. I just don't understand why you would do this. Is there a lamens term explanation, haha or is it already in lamens terms?

 

[Gib Z]

Basically, let 2t+3 = u

Absolute value signs mean, keep the u positive at all costs! RAWR!

so, when u is negative, less than zero, to make it postive stick another negative sign in front right?!

When u is positive, leave it as it is.

So that splits it into 2 bits thatll keep it positive!

-(2t+3) for < 0, 2t+3 for > 0 :D:D

 

[Corkery]

WOW! I actually understand that! thank you so much GIB Z and thank you Mindscrape. You guys rock!

 

[tim_lou]

or you can "read" the function

let f(x)=|x|

basically, you are asked to figure out the graph for
f(2(t+3/2))

the factor of two means 2 times narrower, +3/2 means translation to the left for 3/2 units.

just transform the V shape according to the recipe and you are done.