## How do you find the horizontal and vertical shift?

The vertical shift results from a constant added to the output. Move the graph up for a positive constant and down for a negative constant. The horizontal shift results from a constant added to the input. Move the graph left for a positive constant and right for a negative constant.

How do you write a horizontal shift to the right?

We can express the application of horizontal shifts this way: Formally: given a function f(x), and a constant a > 0, the function g(x) = f(x – a) represents a horizontal shift a units to the right from f(x). The function h(x) = f(x + a) represents a horizontal shift a units to the left.

### How do you shift a function to the right?

In function notation, to shift a function left, add inside the function’s argument: f(x + b) shifts f(x) b units to the left. Shifting to the right works the same way, f(x – b) shifts f(x) b units to the right.

What is the horizontal shift of this equation?

Horizontal Shift Equation The equation indicating a horizontal shift to the left is y = f(x + a). The equation indicating a horizontal shift to the right is y = f(x – a). For example, in order to shift the graph of y = x^2 + 2 to the right 4 places, the equation must be written y = (x-4)^2 +2.

## How do you find the vertical shift?

Step 1: Remember the general form of a trig function. If you divide the C by the B (C / B), you’ll get your phase shift. The D is your vertical shift. The vertical shift of a trig function is the amount by which a trig function is transposed along the y-axis, or, in simpler terms, the amount it is shifted up or down.

What is vertical and horizontal shift?

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.

### What is an example of a vertical shift?

A vertical shift is when the graph literally moves vertically, up or down. The movement is all based on what happens to the y-value of the graph. The y-axis of a coordinate plane is the vertical axis. When a function shifts vertically, the y-value changes.

What shifts a graph to the right?

Thus, adding to the input of a function moves the graph left, and subtracting from the input of a function moves the graph right.

## Why are horizontal shifts opposite?

So you see, they really work the same way, it just looks opposite because the factor a gets moved to the other side.

How do you calculate vertical shift?

If you divide the C by the B (C / B), you’ll get your phase shift. The D is your vertical shift. The vertical shift of a trig function is the amount by which a trig function is transposed along the y-axis, or, in simpler terms, the amount it is shifted up or down.