Been stuck for 6 days, no help !

Question

1) Compare the functions shown below: 

 

 

f(x) 

 

x y 

-3 -27 

-2 -8 

-1 -1 

0 0 

1 1 

2 8 

3 27 

4 64 

g(x) 

 

linear graph with y intercept of negative 1 and x intercept of negative 2

h(x) = (x + 4)2 + 2 

 

What is the correct order of the functions from least to greatest according to the average rate of change on the interval from x = 0 to x = 4? 

f(x), g(x), h(x) 

 

g(x), f(x), h(x) 

 

h(x), g(x), f(x) 

 

g(x), h(x), f(x)

Answer 1

f(x) = - 3x - 5

To find the y -intercept, substitute x = 0 in the above equation.

f(0) = - 3(0) - 5 = - 5

y-intercept of f(x) is -5.

 

g(x) = cos(x)

To find the y -intercept, substitute x = 0 in the above equation.

g(0) = cos(0) = 1, therefore y-intercept is 1.

 

- 3 h(x) = 2 cos(2x − π) + 4

h(x) = - (2/3) cos(2x − π) - (4/3).

To find the y -intercept, substitute x = 0 in the above equation.

h(0) = - (2/3) cos[2(0) − π] - (4/3)

h(0) = - (2/3) (-1) - (4/3) = 2/3 - 4/3 = - 2/3.

y-intercept of h(x) is - 2/3.

 

g(x) = cos(x) has the greatest y-intercept.

 

 

Comments

I cannot stop thanking you. You are awesome :) I have three more questions and I will love if you could help me through. I have tried everything you was the first one that helped me out. Biggest gratitude Compare the functions shown below: f(x) = 3 cos 2x + 4 g(x) cosine graph with points at 0, 3 and pi over 2, 0 and pi, negative 3 and 3 pi over 2, 0 and 2 pi, 3 h(x) x y -6 -11 -5 -6 -4 -3 -3 -2 -2 -3 -1 -6 0 -11 Which function has the greatest maximum y-value? f(x) g(x) h(x) All three functions have the same maximum y-value.

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Thank you. Please ask your questions as new one instead of continue in this post, if you face difficulty please click the below link for asking a new question.

http://www.mathskey.com/question2answer/ask?cat=5

 

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Okay I did

Answer 2

Hi HelpPlease,

Question is not clear,please post clearly.

Comments

Hello, Good morning!! Where are you confused ?

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@bradely

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please check my answer below, i hope it helps a lil

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You have no idea how much you have helped me on this one question. Can you please help me with some more? You are awesome

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glad you like our answer, thank you...

Answer 3

First find the average rate for each function.

Average rate for Function f(x):

Average rate = dy/dx =( y2 - y1)/(x2 - x1) = (64 - 0) / (4 - 0) = 64 /4 = 16

 

Average rate for Function g(x):

linear equation with x and y intercept are x/a + y/b = 1, a nd b are intercepts of x and y respectively

x/(-2) + y/ (-1) = 1

x + 2y = -2

y = -1/2x - 2

Average rate = dy/dx =m = -1/2

 

Average rate for Function h(x):

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

h(0) = (0+4)^2 + 2 = 18

h(4) = (4+4)^2 + 2 = 66

Average rate = dy/dx =( y2 - y1)/(x2 - x1) = (66 - 18) / (4 - 0) = 48 /4 = 12

 

Arrange the average rates least to greatest

-1/2, 12, 16

g(x), h(x), f(x)

Comments

OMG, thank you so much. Can you help me with some more???

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Welcome, ready to answer your questions ;) please ask your questions.

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Compare the functions shown below: f(x) = -3x − 5 g(x) cosine function with y intercept at 0, negative 3 h(x) = 2 cos(2x − π) + 4 Which function has the greatest y-intercept? f(x) g(x) h(x) All three functions have the same y-intercept. I was thinking the answer was A but i am not sure because I am not good at these.