# Review Excercises(Prerequisites for Calculus)

• Aug 31st 2009, 06:50 PM
fezz349
Review Excercises(Prerequisites for Calculus)
Find the (a) domain and b(range), and c(graph the function.)

1. y=|x|-2
3. y=2e^-x - 3
4. y=2sin(3x + Pi) -1
5. y= ln(x-3) + 1

Couple problems i'm trying to figure out. Disregard part C, I've already done that. how do you find the domain, range for these kinds of problems?(process). Any help would be extremely appreciated :)
• Aug 31st 2009, 07:06 PM
fezz349
I know that domain has something to do with the x-values and the range has something to do with the y-values but i'm not exactly sure how to apply this to the problems.
• Aug 31st 2009, 07:15 PM
Chris L T521
Quote:

Originally Posted by fezz349
Find the (a) domain and b(range), and c(graph the function.)

1. y=|x|-2
3. y=2e^-x - 3
4. y=2sin(3x + Pi) -1
5. y= ln(x-3) + 1

Couple problems i'm trying to figure out. Disregard part C, I've already done that. how do you find the domain, range for these kinds of problems?(process). Any help would be extremely appreciated :)

For (1), are there any real numbers that cause it to be undefined? Also, note that $\displaystyle \forall x\in\mathbb{R},\,\left|x\right|\geq0$. So what would you thing the range of $\displaystyle \left|x\right|-2$ is?

For (2), rewrite it as $\displaystyle x^2+y^2=16$. Now, what is the domain and range of that "function"?

For (3), are there any real numbers that cause it to be undefined? Also, note that as $\displaystyle x\to+\infty,\,e^{-x}\to 0$ and $\displaystyle x\to-\infty,\,e^{-x}\to+\infty$. So what do you think the range of $\displaystyle 2e^{-x}-3$ is?

For (4), are there any real numbers that cause it to be undefined? Also note that the amplitude of the wave is $\displaystyle 2$. So what do you think the range of $\displaystyle 2\sin\left(3x+\pi\right)-1$ is?

For (5), Note that as $\displaystyle x\to0^-,\, \ln x\to-\infty$. So what should the domain of $\displaystyle \ln\!\left(x-3\right)+1$ be? From here, it should be obvious what the range is.

Can you try these problems now?
• Aug 31st 2009, 07:43 PM
fezz349
thanks for the pointers, working on them now... by the way what is http://www.mathhelpforum.com/math-he...ee287fb7-1.gif. ???
• Aug 31st 2009, 07:51 PM
Chris L T521
Quote:

Originally Posted by fezz349
thanks for the pointers, working on them now... by the way what is http://www.mathhelpforum.com/math-he...ee287fb7-1.gif. ???

$\displaystyle \forall x\in\mathbb{R},\,\left|x\right|\geq0$ in English says:

For any real number $\displaystyle x$, the absolute value of $\displaystyle x$ is greater than or equal to zero.