Question

HELP PLZ! I do not understand this!!

Let f(x) represent a function.

Which descriptions match the given transformations?

Drag and drop the answers into the boxes.



f(x+1/3) <--------------------->
f(x)−1/3 <--------------------->

Answer Choices:
f(x) is translated 1/3 units up.
f(x) is translated 1/3 units left.
f(x) is vertically compressed by a factor of 1/3.
f(x) is translated 1/3 units right.
f(x) is vertically stretched by a factor of 1/3.
f(x) is translated 1/3 units down.

Answer 1

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

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.

Answer 2

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.