Question

For horizontal transformation of function,
adding to x makes the function go left
subtracting from x makes the function go right

How prove it?

Answer 1

give me an example of a function and ill show you

Answer 2

For example: \[y=x^2\]

Answer 3

There is any general proof?

Answer 4

yes.. the general form of an exponential function is : \[y=-a ^{-x-b}+c\] . the minus in front of the a indicates a reflection in the x axis the - in front of the x indicates a reflection in the y axis. the - in front of the b however indicated the direction of the horizontal shift. if you put any negative number into b... the number will become positive and shift to the right. if you put in any positive number into b the overall number will become negative and will shift to the left. you understand?

Answer 5

in the example u gave me there is no shift taking place if that clarifies things

Answer 6

Yeah, but the proof I'm looking for isn't exactly this one. I wanna prove for every single case where "adding to x makes the function go left". Why not go right?

Answer 7

How to Horizontally Transform a Function

You can transform any function into a related function by shifting it horizontally or vertically, flipping it over (reflecting it) horizontally or vertically, or stretching or shrinking it horizontally or vertically. Let’s go through the horizontal transformations. Consider the exponential function


Take a look at the following graph.


You make horizontal changes by adding a number to or subtracting a number from the input variable x, or by multiplying x by some number.

All horizontal transformations, except reflection, work the opposite way you’d expect:

Adding to x makes the function go left.

Subtracting from x makes the function go right.

Multiplying x by a number greater than 1 shrinks the function.

Multiplying x by a number less than 1 expands the function.

Horizontal translation

For example, the graph of y = 2x+3 has the same shape and orientation as the graph for y = 2x. It’s just shifted three units to the left. Instead of passing through (0, 1) and (1, 2), the shifted function goes through (–3, 1) and (–2, 2). And the graph of y = 2x–3 is three units to the right of y = 2x.

Horizontal shrinking and stretching
For the next two transformations, why don’t you try graphing them on your own.


So, every point on the new function is half of its original distance from the y-axis. The y-coordinate of every point stays the same; the x-coordinate is cut in half. For example,


Multiplying x by a number less than 1 has the opposite effect.


Horizontal reflection

The last horizontal transformation is a reflection over the y-axis.


Note that after the reflection, points are on the opposite side of the y-axis, but remain the same distance from the axis. And original points that lie on the y-axis (the y-intercepts) stay where they are.

Answer 8

http://www.dummies.com/how-to/content/how-to-horizontally-transform-a-function.html