How do you shift and reflect a function?

The function translation / transformation rules:

1. f (x) + b shifts the function b units upward.
2. f (x) – b shifts the function b units downward.
3. f (x + b) shifts the function b units to the left.
4. f (x – b) shifts the function b units to the right.
5. –f (x) reflects the function in the x-axis (that is, upside-down).

How do you shift a function vertically?

We can express the application of vertical shifts this way: Formally: For any function f(x), the function g(x) = f(x) + c has a graph that is the same as f(x), shifted c units vertically. If c is positive, the graph is shifted up. If c is negative, the graph is shifted down.

How do you shift an equation to the right?

To shift, move, or translate horizontally, replace y = f(x) with y = f(x + c) (left by c) or y = f(x – c) (right by c).

What is a shift in algebra?

Vertical shifts are outside changes that affect the output ( y- ) axis values and shift the function up or down. Horizontal shifts are inside changes that affect the input ( x- ) axis values and shift the function left or right.

How do you shift a function horizontally?

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.

What does shift mean in math?

A transformation in which a graph or geometric figure is picked up and moved to another location without any change in size or orientation.

What does shifting look like?

There are certain symptoms when you’re trying to shift that will let you know that you’re getting close. Some of these symptoms include feeling weightless or heavy, tingliness, feeling as though you’re spinning or falling, hearing voices or sounds associated with your DR, seeing flashes of light, etc.