Question

square root function.

Answer 1

We know that we can’t set the function to -4. Cuz that’d make the inroot -1 and u can’t take a square root of -1

Answer 2

That’s our domain.
All real numbers except x can’t equal to -1.

Answer 3

Yes, x can't be less than 3, not inclusive.

Answer 4

For the range, y has to be bigger than 0.... I think

Answer 5

Correct. This is where knowing your function transformations are important.

f(x+h)+k

Answer 6

Wait, can we algebraically figureout the range?

Answer 7

yes of course. Now in some really complex cases algebra won't be enough, then you'll use limits

Answer 8

Show me the algebraic way.. don’t worry about the limits here..

Answer 9

I don’t need to know limits this early in the book

Answer 10

Well what I did here was I just knew the normal behavior for square root functions and I imagined it in my head.
Then I viewed the transformation done here using f(x+h)+k. There is no k value, only an h This means the function was moved left 3 from its parent function.

Now in some cases, there may be a vertical/horizontal stretch, and transformations aren't as useful. I'll show you based on the question.

Answer 11

Nope.. so u just took the normal graph of that function and shifted 3 units to the 3?

Answer 12

Yes

Answer 13

Okie dokie

Answer 14

Precalculus?

Answer 15

This is cal 1

Answer 16

Ah ok

Answer 17

So I need to memorize the graphs of different functions...I see

Answer 18

No, just know the parent functions of these:
1. Linear
2. Quadratic
3. Cubic
4. Quartic
5. Exponential
6. Logarithmic
7. Rational
8. Square root
9. Cube Root
10. Floor function
11. Ceiling function
12. Absolute value
13. Sine, Cos, Tan
14. Piece Wise (Only if you know the 13 above, you'll automatically understand piece-wise)

Answer 19

Okie dokie. Thanks. Let me write everything down..brb

Answer 20

And for rational, know the behavior for 1/x^n where n is both even AND odd. They're parent functions look a bit different (ie 1/x and 1/x^2, then 1/x^3, etc.)

Answer 21

And then know your function transformations, then you can figure out anything out of any graph. This includes the special transformations (phase shift) for sine/cos/tan waves

Answer 22

I used to know the transformation... will memorize that chart by tomorrow.

Answer 23

it's actually here...
https://www.shelovesmath.com/algebra/advanced-algebra/parent-graphs-and-transformations/

Answer 24

brb i need to talk to my roommate for a second. brb :)

Answer 25

So for the domain, can I say the following?

Answer 26

Correct and correct notation

Answer 27

Wooooooooooooow

Answer 28

Wait, why \(y \ge -3\) for \(f(x) = \sqrt{x+3}\)

Answer 29

Should be \(x\), not \(y\)

Answer 30

Oops

Answer 31

I think this time I was the one that read wrong; it should be x

Answer 32

correct

Answer 33

Good catch mate.....gimme a hyfy

Answer 34

And no vertical asymptote?

Answer 35

Also, I don't think I've seen domain of a function \(f\) represented as \( \{ f(x) \} \) before, usually people just write something like \( \mathrm{domain}(f)\) or similar.

\( \{ f(x) \} \) looks like a set with only one(?) element, \(f(x)\)

Answer 36

Eh, I mean I was kinda liberal looking at his notation but I noticed that too. f(x) would go outside, then it would be D:{....} or just interval notation is easier

Answer 37

Sooo just...

Answer 38

I think the more immediate question is....r there NY VERTICAL asymptote?no right?

Answer 39

Any*

Answer 40

Personally I'd just write \( \mathrm{domain}(f) = \{ x \in\mathbb{R} : x \ge -3\} \)

because \( \{ f \} \) looks like a set with the function \(f\) as its element.

Like if \(f(x) = \sqrt{x+3}, g(x) = \sqrt{x-3}, h(x) = 5\sqrt{x}\), then the set \( \{ f, g, h\} \) is a set of functions whose parent function is the square root function.

There are no vertical asymptotes.

Answer 41

Okie dokie

Answer 42

Tomorrow we’ll start working on functions...like adding subtracting multiplying and dividing the functions...should be lit tho