Can a horizontal shift be combined with a vertical shift?

**Vertical and horizontal**shifts can be combined into one expression. Shifts are added/subtracted**to**the x or f (x) components. If the constant is grouped with the x, then it is a**horizontal**shift, otherwise it is a**vertical**shift. A scale is a non-rigid translation in that it does alter the shape**and**size of the graph of the function.

Contents

- 1 How do you stretch horizontally and vertically?
- 2 Do you do horizontal stretch or vertical stretch first?
- 3 How do you do a vertical stretch and compression?
- 4 What order should transformations be applied?
- 5 What letter represents a horizontal shift?
- 6 How do you shift a function horizontally?
- 7 How do you stretch a graph vertically?
- 8 How do you shift horizontally?
- 9 Whats a horizontal stretch?
- 10 How does horizontal stretch work?
- 11 Are vertical stretch and horizontal shrink the same?

## How do you stretch horizontally and vertically?

Key Takeaways

- When by either f(x) or x is multiplied by a number, functions can “stretch” or “shrink” vertically or horizontally, respectively, when graphed.
- In general, a vertical stretch is given by the equation y=bf(x) y = b f ( x ).
- In general, a horizontal stretch is given by the equation y=f(cx) y = f ( c x ).

## Do you do horizontal stretch or vertical stretch first?

When combining horizontal transformations written in the form f(b(x−h)) f ( b ( x − h ) ), first horizontally stretch by 1 b and then horizontally shift by h. Horizontal and vertical transformations are independent. It does not matter whether horizontal or vertical transformations are performed first.

## How do you do a vertical stretch and compression?

How To: Given a function, graph its vertical stretch.

- Identify the value of a.
- Multiply all range values by a.
- If a>1, the graph is stretched by a factor of a. If 0

## What order should transformations be applied?

Apply the transformations in this order:

- Start with parentheses (look for possible horizontal shift) (This could be a vertical shift if the power of x is not 1.)
- Deal with multiplication (stretch or compression)
- Deal with negation (reflection)
- Deal with addition/subtraction (vertical shift)

## What letter represents a horizontal shift?

horizontal and vertical shifts They are one of the most basic function transformations. In the general form of function transformations, they are represented by the letters c and d. Horizontal shifts correspond to the letter c in the general expression. If c is negative, the function will shift right by c units.

## How do you shift a function horizontally?

A General Note: Horizontal Shift Given a function f, a new function g ( x ) = f ( x − h ) displaystyle gleft(xright)=fleft(x-hright) g(x)=f(x−h), where h is a constant, is a horizontal shift of the function f. If h is positive, the graph will shift right. If h is negative, the graph will shift left.

## How do you stretch a graph vertically?

To stretch or shrink the graph in the y direction, multiply or divide the output by a constant. 2f (x) is stretched in the y direction by a factor of 2, and f (x) is shrunk in the y direction by a factor of 2 (or stretched by a factor of ). Here are the graphs of y = f (x), y = 2f (x), and y = x.

## How do you shift horizontally?

The function h(x) = f(x + a) represents a horizontal shift a units to the left. Informally: Adding a positive number after the x inside the parentheses shifts the graph left, adding a negative (or subtracting) shifts the graph right.

## Whats a horizontal stretch?

Horizontal stretches are among the most applied transformation techniques when graphing functions, so it’s best to understand its definition. Horizontal stretches happen when a base graph is widened along the x-axis and away from the y-axis. Understanding the common parent functions we might encounter.

## How does horizontal stretch work?

A horizontal stretch or shrink by a factor of 1/k means that the point (x, y) on the graph of f(x) is transformed to the point (x/k, y) on the graph of g(x).

## Are vertical stretch and horizontal shrink the same?

A vertical compression (or shrinking) is the squeezing of the graph toward the x-axis. if k > 1, the graph of y = k•f (x) is the graph of f (x) vertically stretched by multiplying each of its y-coordinates by k. A horizontal compression (or shrinking) is the squeezing of the graph toward the y-axis.