1) write an absolute value equation that is reflected, vertically shifted 2/3 units down and 1/2 units to the right. 2) write an absolute value equation with a horizontal shift 4 units to the right.

Question 1) Write an absolute value equation that is reflected, vertically shifted 2/3 units down and 1/2 units to the right.

Answer 1):

We know that absolute function is given by y=|x|

reflection happens when we multiply by negative sign so we get

y=-|x|

To get vertical shift down, we subtract so new equation is

y=-|x|-2/3

To get right shift by h unit, we replace x by (x-h) so the new equation is

y=-|x-1/2|-2/3

Hence final answer is

Question2) Write an absolute value equation with a horizontal shift 4 units to the right.

We know that absolute function is given by y=|x|

To get horizontal right shift by h unit, we replace x by (x-h) so the new equation is

Hence final answer is .

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3