TyErd's questions

[TyErd]

whats the easiest and fastest way to sketch this graph:   

[brightsky]

Sketch y = |x + 4| and y = |x - 4| and do addition of ordinates.

[m@tty]

Take the definition of

So,


And,

So with there are three different cases: , and .

.


This isn't the fastest way, though it doesn't take too much longer.

[TyErd]

If    and , find

EDIT: Sorry i forgot to add in the

[m@tty]

What do you want help with?

.

.

[TyErd]

what values can 'a' take in .  I know that the x value cannot be 0 or a negative number. What about 'a'

[m@tty]

Again, take the more familiar exponential form. .

What values can 'a' take here? 'a' can be any real number, including negatives. But in Methods I am fairly sure that you only consider positive bases.

And what you said about x having to be positive. What about, given that there are negative bases, , is it defined?

[TyErd]

no?

[m@tty]

[TyErd]

how come i cant sketch the graph on my calculator?

[moekamo]

Again, take the more familiar exponential form. .

What values can 'a' take here? 'a' can be any real number, including negatives. But in Methods I am fairly sure that you only consider positive bases.

And what you said about x having to be positive. What about, given that there are negative bases, , is it defined?

hmm, isnt really defined for since for fractional values you will keep getting answers in the complex number system since you cannot take square, 1/4, 1/6 etc roots of a negative number in real numbers so there will be a bunch of points but it is not a continuous function. Thats probably why it doesnt graph on a calculator anyway...

[TyErd]

Differentiate:

[Blakhitman]

is the same as



Then it's just simple power rule.



positive powers, you get:

[m@tty]

This is true.

let .



.

[TyErd]

ohk thnx guys i see where i went wrong. thnks!