Question

HELP PLZ! I do not understand this!!

Answer 1

PART 1
If I have graph f(x) then graph f(x + 1/3) would translate the graph 1/3 to the left.

For example, I have f(x) = x².Then
f(x + 1/3) = (x + 1/3)²

I draw the graph of f(x) = x² and the graph of f(x) =  (x + 1/3)² on cartesian plane to know what's the difference between them.


PART 2
If I have graph f(x) then graph f(x) + 1/3 would translate the graph 1/3 upper.

For example, I have f(x) = x².Then 
f(x) + 1/3 = x² + 1/3

I draw the graph of f(x) = x² and the graph of f(x) = x² + 1/3 on cartesian plane to know what's the difference between them.


SUMMARY
f(x+1/3) ⇒⇒ f(x) is translated 1/3 units left.
f(x) + 1/3 ⇒⇒ f(x) is translated 1/3 units up.

Answer 2

Answer:

f(x) is translated 1/3 units left; and f(x) is translated 1/3 units down.

Step-by-step explanation:

Adding or subtracting something to x before the function is applied, as in the first transformation, will shift the graph left or right.  If we add a positive to x the graph shifts left; if we add a negative (or subtract), the graph shifts right.  Since we are adding positive 1/3, the graph will shift left 1/3 units.

Adding or subtracting something to a function (after the function is applied), as in the second transformation, will shift the graph up or down.  If we add a positive, the graph shifts up; if we add a negative (or subtract) the graph shifts down.  Since we are subtracting 1/3 (adding negative 1/3), the graph shifts down 1/3 units.