# Thread: Review Excercises(Prerequisites for Calculus)

1. ## Review Excercises(Prerequisites for Calculus)

Find the (a) domain and b(range), and c(graph the function.)

1. y=|x|-2
2. y= Radical(16-x^2) Radical= Square root symbol and numbers are under radical.
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

2. 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.

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

1. y=|x|-2
2. y= Radical(16-x^2) Radical= Square root symbol and numbers are under radical.
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 $\forall x\in\mathbb{R},\,\left|x\right|\geq0$. So what would you thing the range of $\left|x\right|-2$ is?

For (2), rewrite it as $x^2+y^2=16$. 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 $x\to+\infty,\,e^{-x}\to 0$ and $x\to-\infty,\,e^{-x}\to+\infty$. So what do you think the range of $2e^{-x}-3$ is?

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

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

Can you try these problems now?

4. thanks for the pointers, working on them now... by the way what is . ???

5. Originally Posted by fezz349
thanks for the pointers, working on them now... by the way what is . ???
$\forall x\in\mathbb{R},\,\left|x\right|\geq0$ in English says:

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