Question

Compare the functions shown below.

Answer 1

Which function has the greatest y-intercept? (2 points)


f(x)

g(x)

h(x)

All three functions have the same y-intercept.

Answer 2

Don't know what f, g, and h are. However, if you look at them mathematically, you should be able to find the y intercepts.

Answer 3

Help?

Answer 4

Like I said, I don't know what f, g, and h are. How can I help if I do not know what the fuctions are?

Answer 5

The functions are in the graph attached

Answer 6

@VeritasVosLiberabit

Answer 7

gamer mccormick is looking for the actual function eg. y=x

Answer 8

They didn't give me that just a graph

Answer 9

they can do anything if you don't know the function itself

Answer 10

I see 5 lines in the attached graph, none of which have any markings as to which function they are.

Answer 11

f(x) = 4x + 5
h(x) = 3 sin(2x + π) - 2

Answer 12

Those are definitely not the same funtions as in the picture

Answer 13

That is what they gave

Answer 14

Maybe you have to assume that the functions have asymptotes and approach some x value

Answer 15

If that is the case the only thing I could say is the middle one has the largest y-intercept. But I have no idea which funtion that corresponds to

Answer 16

In a linear function: \(y=mx+b\) the b is the y intercept
In the sine fuction \(y=A\sin(x+h)+b\) the b is the y intercept

It changes for others, but in those two, the b spot is what you need to look at.

Answer 17

See second attachment

Answer 18

g(x)

Answer 19

And for g(x), well, you can see the y intercept on that agraph.

Answer 20

So is the answer B then?

Answer 21

Well, given what I have pointed out, what are thr three y intercepts?

Answer 22

I am not sure? How do I plug it in?

Answer 23

Start with the \(f(x) = 4x + 5 \). What is the y intercept for that? It is a linear equation and should be the simplest one.

Answer 24

5

Answer 25

OK. So, the next one is the graph of \(g(x)\) Where does that intercept y?

Answer 26

I am not sure really?

Answer 27

It is on the graph. Where does it hit the y axis?

Answer 28

Not sure

Answer 29

Can you see the y axis on the picture?

Answer 30

I don't know

Answer 31

OK.

The x axis or abscissa is the horizontal line with numbers on it. In this case, they are assorted things with \(\pi\) in them.

The y axis or ordinate is the vertical line with numbers on it. In this case, they are integers.

Answer 32

At (0,2)

Answer 33

Yes. It has to do with the definition of a function. For any X value there is 1 and only one Y value. So it can't loop over off the shown part of the graph and mess you up because they told you it is a function.

Answer 34

OK. So, what is the y intercept of the last one? The fact it is shifted might make it a little tricky.

Answer 35

Don't know, this is taking really long and I have 41 assignments with questions like these

Answer 36

There is some logic you can use if you know what the amplitude of the trig function is.

Answer 37

explain

Answer 38

The hx one has a y intercept of -2

Answer 39

On sine, the amplitude tells you the highest and lowest points before things are shifted. So on \(A\sin x\) A is the amplitude. If it was say 20, then the highest and lowest points would be 20 and -20 before any shifts. On yours it is 3. And the shift at the end of yours is -2. So, the highest point that graph ever reaches is 3-2=1. No matter what the y int is, it can not be more than 1.

Answer 40

So, of 5, 2, and -2, which is the highest y intercept?

Answer 41

So it is A

Answer 42

Yep.
https://www.desmos.com/calculator/q6cyithltk

Answer 43

I have another question

Answer 44

How do I solve this, I don't know what g(x) is?

Answer 45

Is it A?

Answer 46

See what \((0,y_1)\) and \((4,y_2)\) for each function. Then do \(|y_2-y_1|\) that will get you the average rate of change for those functions over that period. The reason I use the absolute value is because you want rate of change, not rate and direction.

Answer 47

fx rate of change is 64

Answer 48

Yes.

Answer 49

gx is -2

Answer 50

Don't know what hx is

Answer 51

That is rate and direction. For just rate it is 2.

Answer 52

\(h(x)=(x+4)^2+2\)

\(h(0)=(0+4)^2+2\)
\(h(0)=(4)^2+2\)

and

\(h(4)=(4+4)^2+2\)
\(h(4)=(8)^2+2\)

Find those.

Answer 53

hx=48

Answer 54

Help?

Answer 55

D is the answer

Answer 56

Well, g(x) is changing slowest, and f(x) the fastest.

Answer 57

I have more

Answer 58

Is it h(x)?

Answer 59

Trig functions will be different, but for the \(x^n+x^{n-1}+...+x+k\) functions, the MOST they will have is n intercepts with the x axis. So the higest degree is the most they could have. They can also have less if they have a hump that just touches or does not touch.

Answer 60

So how do I solve this?

Answer 61

Well, you can use that fact to know the most that h(x) has. Then look at f(x) and g(x).

Answer 62

Does anyone know which function had the most intercepts

Answer 63

Well, did you look at what I suggested to them for how to solve it?

Answer 64

yea, it doesn't matter right now, i thought it was fx but that was wrong.

Answer 65

For future people the answer was h(x)!