If anyone knows how to do any of these 11 problems please help.

3.) What is the average rate of change of f(t) = t^2 – 2t between t = 2 and t = 2+h

4.) Describe the transformations from f(x) = x^3 to g(x) = -(x-1)^3

5.) What transformation occurs if f(x) becomes f(3x)

6.) Translate f(x) = x^2 – 2x +3 left 2 units. Write in standard form.

7.) Horizontally stretch g(x) = 8x^2 – 4x + 6 by a factor of 2. Write in standard form.

8.) Let h(x) = x^2 – 1, where x less then or equal to 0. 2x + 4, where x greater than 0.

9.) Evaluate h(-2) and (1). (Use the problem 8)

11.) f(x) = x^3 + 5, find the inverse function.

13.) f(x) = square root of x^2 -9 and g(x) = square root of g(x) = 25 – x^2. What is the domain of f + g?

14.) On which intervals is f(x) = 3x^4 – 10x^2 + 5x – 3 increasing?

15.) A isosceles triangle has a perimeter of 12 units and a base of b. Write a function for the area of the t in terms of base b. ( I think I got this one just want to be sure)

Masters Student in Mathematics here. I can help with any/all of these problems. Describe exactly what help you need because most of these problems are basic Algebra questions. Ill write some hints below to each problem but you need to try on your own and let me know if you run into problems.

3. Recall Avg rate of change eq. A(x)=( F(x)-F(a) )/( x-a)
4. look at change from f(x) to g(X) .... we can see a - (which flips eq) a (x-1) which translates funct left or rt
5. plug 3x in for x in f(x) so just f(3x)= (3x)^3 thus we can see eq will stretch by 3
6. see prob 4 we note how to translate
7. look up transf in book not that hard to figure out how to stretch.
8. peicewise functions just evaluate that function over only given domain and then it turns into other function
9. let x=-2 and plug into h(x) so h(-2)= (-2)^2-1=3 while h(1)= 2(1)+4 = 6
11. to find inverse just recall f(x)=y so y=x^3+5 .... just solve for x and that is your inverse function
13. Add f(x)+g(x) then look at domain of your function

14. look at it for yourself and see when y values are increasing and over what (x) values they are inc over
https://www.desmos.com/calculator
15 . show me what you have bc question is written oddly

Appreciate it. I'm getting on it now.

3.) What is the average rate of change of f(t) = t^2 – 2t between t = 2 and t = 2+h
Calculate the output of that function for the 2 different inputs provided. These 2 points define a line. The average rate of change is the slope of that line (use the old slope formula).

4.) Describe the transformations from f(x) = x^3 to g(x) = -(x-1)^3
x^3 -> (x-1)^3 is shifting one to the right
(x-1)^3 -> -(x-1)^3 is reflection about the x axis

5.) What transformation occurs if f(x) becomes f(3x)
shrink by factor of 3 (horizontal shrink)

6.) Translate f(x) = x^2 – 2x +3 left 2 units. Write in standard form.
(x+2)^2 - 2(x+2) + 3, you can simply this on your own

7.) Horizontally stretch g(x) = 8x^2 – 4x + 6 by a factor of 2. Write in standard form.
8(x*0.5)^2 - 4(x*0.5) + 6, you can simply this on your own

8.) Let h(x) = x^2 – 1, where x less then or equal to 0. 2x + 4, where x greater than 0.
not a question, IMO

9.) Evaluate h(-2) and (1). (Use the problem 8)
hesitant to answer since 8 is confusing

11.) f(x) = x^3 + 5, find the inverse function.
solve for x, then switch the x and f(x) in the function

13.) f(x) = square root of x^2 -9 and g(x) = square root of g(x) = 25 – x^2. What is the domain of f + g?
x>=3 or x<= -3(from the first equation), and x <=5 or x>=-5 (from the 2nd equation); i think you can do the rest

14.) On which intervals is f(x) = 3x^4 – 10x^2 + 5x – 3 increasing?
heh not actually sure how to get this answer without calculus, which of course would not help you

15.) A isosceles triangle has a perimeter of 12 units and a base of b. Write a function for the area of the t in terms of base b. ( I think I got this one just want to be sure)
if we bisect the triangle it will give us 2 identical right triangles. The base of one of these triangles will be (1/2)b, one of the sides will be unknown, and the hypotenuse will be (1/2)*(12-b). Now you have 2 sides of a right triangle expressed (using b). Pythagoras theorem will give you the unknown side (which is also the height of the original triangle) in terms of b. Now you have the base of the original triangle in terms of b (it is b), and the height in terms of b (from Pythagoras theorem), so you can get calculate the area as these 2 numbers multiplied together * 0.5 using the old school (1/2)* base* height idea.

This post was edited by Azrad on Sep 19 2013 06:36pm