Question

Quick review help for Trig? 2 questions?

Answer 1

First one:
What is the correct order of the functions from least to greatest according to the rate of change on the interval from x = -1 to x = 3?
f(x), g(x), h(x)
g(x), f(x), h(x)
h(x), g(x), f(x)
g(x), h(x), f(x)

Here is the graph/charts:

Also, I think the answer is C, but I'm really not sure, which is why I'm asking.

Answer 2

Hold on, it didn't attach the whole picture.

Answer 3

f(x) = (x + 3)^2 - 2, g(x) is the graph, and I will post h(x) in just a second.

Answer 4

Ok, for g(x), the rate of change is constant because it is linear. The rate of change will be the slope. Just a little note.

Answer 5

h(x) are the points: (-3,2) (-2,7) (-1,14) (0, 23) (1,34) (2,47) (3,62)

Answer 6

Ok. Let's do the easy one first. Can you figure out the slope of g(x)?

Answer 7

I believe it's 1/3, but I'm also thinking it's 3/1. I'm just really stressing out right now, I'm sorry.

Answer 8

It's cool. Yes, the slope is 1/3 for g(x). Therefore, the rate of change og g(x) is 1/3. We'll make a note of that.

Answer 9

Now, let's find the rate of change of h(x). We'll need a formula for that:
\[avg. rate of change = \frac{f(b) - f(a)}{b-a}\]

Answer 10

Doesn't this look like the slope formula? It's basically what it is. What is the slope of a line that joins too points on a graph.
So, for h(x), what's the values of the function when x = -1 and 3?

Answer 11

It does. Oh, so I need to find the slope between the points (-1, 14) and (3, 62), right?

Answer 12

I got 12.

Answer 13

Correct. That will be the average rate of change of the h(x) on that interval.

Answer 14

Cool, I don't have a handy calculator, so I'll take your word lol. Now we have:
rate of change of g(x) = 1/3
rate of change of h(x) = 12

Now we need the rate of change of f(x).

Answer 15

There only gave us the function, though. We need to find the value at x = -1 and 3. Then, use the formula again to find the average rate of change.

Answer 16

My iTouch is lost amongst all of my trig papers lol. I used the Google calculator.

Answer 17

lol

Answer 18

Hmm, I can't remember how I need to do that.

Answer 19

Could I graph it and find the values that way?

Answer 20

f(x) = (x+3)^2 - 2
Plug in -1 for x to find the value. Plug in 3 for x to find that value.

Answer 21

No need for graphing.

Answer 22

Oh, I'm sorry. For some reason I always take the hard route.

Answer 23

For x = -1 I got the point (-1, 2). Let me check the second one real quick.

Answer 24

That is correct.

Answer 25

For x = 3, I got the point (3, 34). Now do I do the same thing I did before by subtracting the points, like in the formula you posted earlier?

Answer 26

Yep :3

Answer 27

Okay, I got 8.

Answer 28

So the answer would be B, right?

Answer 29

So did I in my head lol. This is what we have now:
rate of change f(x) = 8
ROC g(x) = 1/3
ROC h(x) = 12

Answer 30

Correct.

Answer 31

Thank you so much for going through that with me. Would you have time to help me with one more?

Answer 32

Sure.

Answer 33

Thank you! :)
For this question, I need to find which function has the most y-intercepts. I have two graphs, one for g(x) & h(x), and for f(x) I'll type it out real quick before I attach the graphs.

Answer 34

A graph would be the most helpful for this lol.

Answer 35

\[f(x) = x ^{3} + 2x ^{2} - 4x - 3\]

Answer 36

g(x)

Answer 37

h(x)

Answer 38

For this one, I'm leaning towards f(x) as a guess.

Answer 39

The most y-intercepts, or x-intercepts?

Answer 40

Most x-intercepts. I'm sorry about that.

Answer 41

Ok, let's look at the graphs first. An x-intercept is where the graph crosses the x axis.
Let's look at g(x). How many times do you see it cross the x axis?

Answer 42

It crosses 4 times.

Answer 43

And for h(x), it crosses 3 times.

Answer 44

Good, let's make a note for both of them. Now, f(x).

\[f(x) = x ^{3} + 2x ^{2} - 4x - 3\]

Answer 45

It would be best to graph it. If not, we would have to solve for x when y = 0. Remember, x-intercepts occur at y = 0.

Answer 46

I have GeoGebra up, so I will be back in just a second.

Answer 47

It also crosses the x-axis three times, right about the areas of x = -3, x = -0.75, and x = 1.5.

Answer 48

So the answer would be g(x), correct?

Answer 49

Correct.

Answer 50

Thank you so much! I really appreciate you taking the time to help me!

Answer 51

No problem.

Answer 52

Have a good afternoon, and take care! :)