Question

What is the average rate of change for the relation shown below between x = -2 and x = 2?

Answer 1

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Answer 2

PLEASE HELP ME @ShadowLegendX

Answer 3

Do you know how to make a table for a relation?

Answer 4

no not really

Answer 5

draw a vertical line through -2 on the x axis. Where does this vertical line cross the parabola?

Answer 6

-2,8

Answer 7

use parenthesis

(-2,8)

Answer 8

do the same for x = 2

Answer 9

(2,0)

Answer 10

so they want you to find the slope of the line through the two points (-2,8) and (2,0)

Slope Formula
\[\Large m = \frac{y_2 - y_1}{x_2 - x_1}\]

Answer 11

-2 is the answer

Answer 12

but it says to put the answer in fraction form..

Answer 13

yes -2 is the answer. If your teacher wants it in fraction form, then write it as -2/1

Answer 14

since x/1 = x

Answer 15

ok and this is another question. the one about the banquet that I got mixed up in

Answer 16

A banquet hall charges $9.50 per person if the group size is 25 people or less and a $650 flat rate if the group size is more than 25 people.


Which function represents the cost of hosting a party at that banquet hall?

Answer 17

f(x)=9.50x+650

Answer 18

f(x)=650-9.50x^2

Answer 19

f(x)=650(x-25)+9.50

Answer 20

the attachment isn't working. I'm not sure why

Answer 21

hold on I'm trying to find a way to get it on here

Answer 22

ok I can't get the picture but this is what it looks like

Answer 23

f(x)={ 9.50x 0 <= x <= 25
650 25

Answer 24

Sounds like it looks like this

\[\Large f(x) = \begin{cases}9.50x \ \ \ \text{ if } 0 \le x \le 25\\650 \ \ \ \text{ if } x > 25\end{cases}\]

is my assumption correct?

Answer 25

yes pretty much

Answer 26

so the first part says "if x is between 0 and 25, then the function is f(x) = 9.50x"

the second part says "if x is larger than 25, then f(x) = 650"

Answer 27

f(x) changes depending on what x is

Answer 28

okay

Answer 29

does that make sense?

Answer 30

yes so far

Answer 31

Do you see how that models the cost function? Do you see how it takes care of both cases?

Answer 32

yes I can see that

Answer 33

so that would be the answer

Answer 34

so it would be the second one?

Answer 35

The whole thing

\[\Large f(x) = \begin{cases}9.50x \ \ \ \text{ if } 0 \le x \le 25\\650 \ \ \ \text{ if } x > 25\end{cases}\]

is considered one function. It's called a piecewise function.

Answer 36

it's comprised of two different pieces to make it one big function

Answer 37

Think of taking apart 2 cars and joining them together to form one bigger car

Answer 38

ohhh ok I am aware of piecewise functions. this makes a lot more sense now

Answer 39

you must love working on math since you've been helping me for the past few hours haha

Answer 40

it's a lot of fun lol

Answer 41

I'm trying to finish an assignment but I'm just so confused on a ton of them I don't even know where to begin :(

Answer 42

ok what other question did you have?

Answer 43

The parabola graphed below represents a side view of a parabolic microphone dish. The directrix is drawn in as well. The end of the microphone is placed on a feedhorn that will need to be placed at the focus of the parabola to pick up the sound. The scale of the graph is in inches.


Based on the graph, the engineers should make the feedhorn _____ inches long.


Enter your answer as the number that correctly fills in the blank in the previous sentence.

Answer 44

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Answer 45

would the correct answer be 4?

Answer 46

To be honest, I'm not exactly sure what they're asking. It sounds like they want you to place the feedhorn at the focus so if you want it to connect to the parabola, then yes, it would be 4 inches. This is because the distance from vertex to directrix is also 4 inches.

Answer 47

ok its fine. next question.Given f(x) = 2x2 + 2x and g(x) = x + 1, find the function (f/g)(x).

Answer 48

I know the answer is 2x but does x= 0 or -1 ??

Answer 49

the denominator is x+1

it cannot be zero. If it were, then x+1 = 0 leads to x = -1

If x = -1,then the denominator is 0. To avoid dividing by zero, we must add on the restriction that \(\Large x \ne -1\)

Answer 50

Which exponential model described below has the smallest y-intercept?

Answer 51

y=6^x+4

Answer 52

a model describes a sample that doubles every hour for x hours.

Answer 53

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Answer 54

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Answer 55

when you write `y=6^x+4` do you mean \(\Large 6^{x}+4\) or do you mean \(\Large 6^{x+4}\)

Answer 56

the first one u put

Answer 57

x is the exponent of 6

Answer 58

what are you thinking on this one? were you able to eliminate a few options?

Answer 59

I removed the t-chart

Answer 60

why did you remove the t-chart ? what's your thinking on that decision?

Answer 61

wait hold on I think that actually might be the correct answer

Answer 62

since it has the smallest x-value which is 0

Answer 63

the y intercept happens when x = 0. They want you to find the smallest y value when x = 0. So you'll compare the different y intercepts of the functions

Answer 64

so the y-int would be 4

Answer 65

on the t-chart? or are you looking at the graph now?

Answer 66

on the t chart

Answer 67

look at where x = 0. What is the paired y value here?

Answer 68

64

Answer 69

so the y intercept here is 64

ie, the point (0,64)

Answer 70

correct

Answer 71

what's the y intercept of the graph?

Answer 72

(0,3)

Answer 73

oh this looks like the correct answer

Answer 74

yes! that was the correct answer

Answer 75

yes it is the correct answer. If you plugged in x = 0 into 6^x + 4, you'd find that y = 5

Answer 76

2(10^3x ) = 24 how can I make this into a logarithm

Answer 77

The equation given to you is this? or no?

\[\Large 2\left(10^{3x}\right) = 24\]

Answer 78

yes

Answer 79

the first thing I would do is divide both sides by 2

Answer 80

what do you get when that happens?

Answer 81

(10^3x)=12

Answer 82

yes. Use parenthesis to show that 3x is in the exponent

10^(3x) = 12

Answer 83

what comes next?

Answer 84

Im confused. would it be log12=

Answer 85

that's part of it

Answer 86

you apply logs to both sides or convert to log form

Answer 87

so is log12 correct?

Answer 88

as part of the answer?

Answer 89

\[\Large 10^{3x} = 12\]
turns into
\[\Large 3x = \log(12)\]
where the log is base 10

Answer 90

oh ok so u just flipped the log to the other side?

Answer 91

is that the most simplified version of the answer?

Answer 92

does your teacher want you to solve for x?

Answer 93

they just want the most simplest form of that equation

Answer 94

@jim_thompson5910

Answer 95

so it sounds like they want to solve for x. So you can divide both sides by 3 or multiply both sides by 1/3

Answer 96

x =log(4)