Question

can someone go over a few of these with me and please explain them? I don't get them at all ....
(a) State the domain of the function.
(b) Graph the function.
h(x) = -3x − 5, −1≤ x < 3

Answer 1

Domain of the function is the values x can take.
The problem states −1≤ x < 3 and that is the domain of the function.
Sometimes it is also written as [-1, 3). The left side is a bracket meaning -1 is included and the right one is a parenthesis meaning 3 is NOT included.

Answer 2

For part b) you just put a few values of x and find h(x). Remember h(x) is same as y.
So you find a few (x,y) values and graph them.
Remember the function should not go to the left of x = -1 or go past x >= 3

Answer 3

h(x) is y
and is f(x) is x?

Answer 4

how do you know that's the domain?

Answer 5

−1≤ x < 3?

Answer 6

Here h(x) is y. In other problems f(x) is y. The latter is the one most frequently used.

Answer 7

how do you know which ones are y? and how do you know the latter one is the most frequently used?

Answer 8

Because it is given in the problem. They state h(x) = -3x − 5, −1≤ x < 3
It means the function h(x) is define ONLY for x greater than or equal to -1 and less than 3.
−1≤ x < 3 is the domain.

In this problem h(x) = -3x − 5
So on the graph the x values will be along the horizontal line, the x axis.
and the h(x) values will be along the vertical line, the y axis.

In some other problem, f(x) may be define as f(x) = 2x + 7. In this problem the x values will be along the x axis and the f(x) values will be along the y axis. So y will be f(x) for this example.

Answer 9

for instance what if its - 3/2x+6 - the one we just did before has a comma so I can see the latter being the domain but what about this one?

Answer 10

If they don't specify a domain in the problem you can look at -3/2x + 6 and see what all values x can take. x can be anything. There is no restriction. So the domain for x will be:
-infinity < x < +infinity.

Answer 11

how do we know there is no restriction? What part of the problem says that?

Answer 12

so that problem doesn't state a domain? -3/2x + 6? and that's why it can be -infiniti,<x<infintiti?

Answer 13

If the problem gives you a domain they are telling you their function is valid ONLY in the domain they give you. You cannot evaluate the function outside the domain because the function is not defined outside the domain.

If they don't give you a domain then you can look at the function and see if there are any value of x that would give us trouble. For example, If f(x) = 1 / (x - 2)
Then x cannot be 2 because you will be dividing by zero when x = 2. Otherwise there is no restriction placed on x. So the domain will be: (-infinity, 2) or (2, +infinity).

Answer 14

If the problem is f(x) = 8x + 3
f(x) can be found for all values of x. There is no restriction. So we can say the domain is: (-infinity, +infinity). Absolutely no restrictions on what x can be.

Answer 15

because there is no domain stated?

Answer 16

Yes, if no domain is stated then you can take a look at the function to see if the function can be evaluated for all values of x. If so, the domain is -infinity < x < infinity

Answer 17

for some reason my mind doesn't get around this stuff! like this one: g(x) =| x − 3| how does one exactly look at these and figure out how to execute them?
The above function doesn't have a specified domain? so it would be -infinity < x < infinity?

Answer 18

But you don't have to state the domain is (-infinity, infinity) every time you come across a function that can be evaluated for all values of x. State it only if they ask you what the domain is.

Answer 19

and how do you exactly know when a domain is stated? what will it state in the problem?

Answer 20

Here in this problem it explicitly states:
−1≤ x < 3
That is your domain. It says x has to be greater than equal to -1 and less than 3. That is your domain.

Answer 21

Yes, for g(x) =| x − 3| we can evaluate g(x) for ALL values of x. There is no restriction on x. So the domain will be (-infinity, infinity). Domain can also be stated as:
-infinity < x < infinity

Answer 22

ohhhh

Answer 23

and then to graph it i plug in 0 or 1 for x?

Answer 24

what about : x^3 + 1

Answer 25

im starting to get it =)

Answer 26

h(x) = -3x − 5 and −1≤ x < 3
So I will pick a few values of x and make sure the values are in the domain.
So x = -1, 0 and 1 are good. They are all greater than or equal to -1 and less than 3.
Evaluate h(x) for those three x values.
Plug in x = -1, 0 and I get:
h(-1) = (-3)(-1) - 5 = -2
h(0) = (-3)(0) - 5 = -5
h(1) = (-3)(1) - 5 = -8
So the points are: (-1, -2) (0, -5) (1, -8)
Just plot them. It will be a straight line.

Answer 27

I don't think x^3 + 1 has a domain of -infiniti and infiniti

Answer 28

Why not? Is there any value of x for which (x^3 + 1) cannot be evaluated?

Answer 29

If f(x) = x^3 + 1
then the domain is -infinity < x < infinity

Answer 30

OOOhhh I c

Answer 31

1 more if that's okay

Answer 32

go ahead.

Answer 33

f (x) = \[\sqrt{?}\]x − 3

Answer 34

\[\sqrt{x-3}\]

Answer 35

Is it \[\Large f(x) = \sqrt{(x - 3)}\]

Answer 36

there are no ( ) in them

Answer 37

Here the parenthesis does not matter.
Do you see any restrictions that should be placed on x?
Ask yourself this: If I put in various values of x such as 0, 1, 2, 3, 4, .... -1, -2, -3, -4, ... etc. will I be able to evaluate f(x) for all those values of x?
Or should x not have certain values?

Answer 38

3?

Answer 39

because you cant have 0 in a square root?

Answer 40

No. You can have 0 in a square root. What you cannot have is a negative inside a square root.

Answer 41

ohhh so you don't want anything to make it negative so 3-3 is 0 but 2-3 is -1 so it would be anything less then 2?

Answer 42

x - 3 is inside a square root. We should not have negative inside a square root. That means x - 3 must always be greater than or equal to zero.
\[x - 3 \ge 0\]
Add 3 to both sides:
\[x \ge 3\]
So the domain is:
\[3 \le x < \infty \]
The domain can also be written as:
\[[3, \infty)\]

Answer 43

ohhhh okay. your good at these.

Answer 44

i can go on for hours but I don't want to take up too much of your time. I really appreciate you helping me

Answer 45

Glad to be able to help.