write a function that is shifted 2 units up from the function f(x)=|x|+3

Write a function that is shifted 4 units down from the function f(x)=|x-3|+1

to shift "up" 2 units, add 2 to the function

f(x) = |x| + 3 + 2
f(x) = |x| + 5

What do you think we should do if we shift it 4 units down ?

To shift a function up or down, you need to add or subtract the desired amount from the original function.

1. For the function f(x) = |x| + 3 shifted 2 units up, you can use the following formula:

g(x) = f(x) + 2

Substituting f(x) into the equation, we get:

g(x) = |x| + 3 + 2

Therefore, the function that is shifted 2 units up is:

g(x) = |x| + 5

2. For the function f(x) = |x - 3| + 1 shifted 4 units down, you can use the following formula:

g(x) = f(x) - 4

Substituting f(x) into the equation, we get:

g(x) = |x - 3| + 1 - 4

Therefore, the function that is shifted 4 units down is:

g(x) = |x - 3| - 3

To shift a function vertically, you need to add or subtract a constant value to the function. In this case, we want to shift the functions up or down.

For the first function, f(x) = |x| + 3, to shift it 2 units up, you need to add 2 to the function. Therefore, the shifted function would be:

g(x) = |x| + 3 + 2
= |x| + 5

So, the shifted function is g(x) = |x| + 5.

For the second function, f(x) = |x - 3| + 1, to shift it 4 units down, you need to subtract 4 from the function. Therefore, the shifted function would be:

h(x) = |x - 3| + 1 - 4
= |x - 3| - 3

So, the shifted function is h(x) = |x - 3| - 3.