I need help with my math hw! Please!

[KeroroK]

Hello, I've been stuck on these homework questions. I've already watched videos and read my textbook , but I am still lost. How would you solve these problems?

1. abs(abs(x-1)-3) = 4 , find all real solutions.

2. A step function is a piece-defined function that is constant on each piece.
A famous step function is the signum function.
{1 x>0
sgn(x)= {0 x=0
{-1 x<0
On a separate axes, plot sgn(x), sgn(x)^2, sgn(x)x, and sgn(x)x^2. Do you know any of these functions by another name?

3. Find a step function with domain R, that passes through (1,1), (2,2), and (3,6).

4. Find a step function f(x) with domain R, such that abs(f(x) - x) <= 1 holds for all x.

5. Find a step function f(x) with domain R, such that abs(f(x) - x) <= 0.5 holds for all x.

Thanks so much!

 

[HallsofIvy]

Hello, I've been stuck on these homework questions. I've already watched videos and read my textbook , but I am still lost. How would you solve these problems?

1. abs(abs(x-1)-3) = 4 , find all real solutions.

Let y= abs(x-1)= 3 so the problem becomes |y|= 4. What are the two possible values for y?

2. A step function is a piece-defined function that is constant on each piece.
A famous step function is the signum function.
{1 x>0
sgn(x)= {0 x=0
{-1 x<0
On a separate axes, plot sgn(x), sgn(x)^2, sgn(x)x, and sgn(x)x^2. Do you know any of these functions by another name?

Have you at least graphed sgn(x)? sgn(x)^2 should be very easy. What is sng(x)^2 for all positive x? For all negative x? But be careful! sgn(0)^2= 0^2= 0! It is "sgn(x)x" that you should know "by another name".

3. Find a step function with domain R, that passes through (1,1), (2,2), and (3,6).

Do you know what a "step function is? There are many answers to this problem but one very simple answer- Take f(x) equal to a single number for all x less than x, another number for x greater than or equal to 1 and less than 2. a third number for x greater than or equal to 2 and less than 3 and a fourth number for x greater than 3. What numbers?

4. Find a step function f(x) with domain R, such that abs(f(x) - x) <= 1 holds for all x.

Again, if you know what a step function is, this should be simple. Just take the "basic step function" (sometimes called the "floor function"), f(x) equal to the largest integer less than or equal to x, and subtract a constant.

5. Find a step function f(x) with domain R, such that abs(f(x) - x) <= 0.5 holds for all x.

If your constant in (4) was large enough, you could use the same example as in (3)!

Thanks so much!

In the future it would help us to give more useful hints if, instead of just listing problems, you showed us what you already understand about each problem, what you have tried on each and where you got stuck.

 

[Deleted member 4993]

Hello, I've been stuck on these homework questions. I've already watched videos and read my textbook , but I am still lost. How would you solve these problems?

1. abs(abs(x-1)-3) = 4 , find all real solutions.

2. A step function is a piece-defined function that is constant on each piece.
A famous step function is the signum function.
{1 x>0
sgn(x)= {0 x=0
{-1 x<0
On a separate axes, plot sgn(x), sgn(x)^2, sgn(x)x, and sgn(x)x^2. Do you know any of these functions by another name?

3. Find a step function with domain R, that passes through (1,1), (2,2), and (3,6).

4. Find a step function f(x) with domain R, such that abs(f(x) - x) <= 1 holds for all x.

5. Find a step function f(x) with domain R, such that abs(f(x) - x) <= 0.5 holds for all x.

Thanks so much!

Looks like you do not understand the concept of absolute value function very well.

Can you plot the following functions:

f(x) = abs(x)

and

f(x) = x

What is the difference between the two graphs?

Are the ranges and the domains of those functions same?