How to calculate horizontal and vertical graph stretches?

- Horizontal And Vertical
**Graph**Stretches And Compressions (Part 1)**The**general formula is given as well as**a**few concrete examples. y = c**f**(**x**), vertical stretch,**factor of**c; y = (1/c)**f**(**x**), compress vertically,**factor of**c; y =**f**(cx), compress**horizontally**,**factor of**c; y =**f**(**x**/c), stretch**horizontally**,**factor of**c; y = –**f**(**x**), reflect at**x**-axis

Contents

- 1 How do you stretch a graph horizontally by a factor of 3?
- 2 How do you stretch a graph horizontally?
- 3 How do you write a horizontal stretch by a factor of 2?
- 4 How do you find the factor of a horizontal stretch?
- 5 Whats a horizontal stretch?
- 6 What is a horizontal stretch?
- 7 How do you find the stretch factor of a graph?
- 8 How do you do a horizontal stretch and compression?
- 9 How do you translate a graph horizontally?
- 10 What is a horizontal shrink by 1 2?
- 11 Why are horizontal stretches opposite?

## How do you stretch a graph horizontally by a factor of 3?

If g(x) = 3f (x): For any given input, the output iof g is three times the output of f, so the graph is stretched vertically by a factor of 3. If g(x) = f (3x): For any given output, the input of g is one-third the input of f, so the graph is shrunk horizontally by a factor of 3.

## How do you stretch a graph horizontally?

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 ).

## How do you write a horizontal stretch by a factor of 2?

Thus, the equation of a function stretched vertically by a factor of 2 and then shifted 3 units up is y = 2f (x) + 3, and the equation of a function stretched horizontally by a factor of 2 and then shifted 3 units right is y = f ( (x – 3)) = f ( x – ).

## How do you find the factor of a horizontal stretch?

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). Consider the following base functions, (1) f (x) = x^{2} – 3, (2) g(x) = cos (x).

## 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.

## What is a horizontal stretch?

A horizontal stretching is the stretching of the graph away from the y-axis. A horizontal compression (or shrinking) is the squeezing of the graph toward the y-axis. • if k > 1, the graph of y = f (k•x) is the graph of f (x) horizontally shrunk (or compressed) by dividing each of its x-coordinates by k.

## How do you find the stretch factor of a graph?

1 Answer

- Refer to: y=af(b(x−h))+k.
- A vertical stretch is the stretching of a function on the x-axis.
- A horizontal stretch is the stretching of a function on the y-axis.
- For example:
- b=12.
- To vertically stretch we use this formula:
- To horizontally stretch we use this formula:
- x1=x12.

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

If the constant is between 0 and 1, we get a horizontal stretch; if the constant is greater than 1, we get a horizontal compression of the function. Given a function y=f(x) y = f ( x ), the form y=f(bx) y = f ( b x ) results in a horizontal stretch or compression.

## How do you translate a graph horizontally?

Horizontally translating a graph is equivalent to shifting the base graph left or right in the direction of the x-axis. A graph is translated k units horizontally by moving each point on the graph k units horizontally. g(x) = f (x – k), can be sketched by shifting f (x) k units horizontally.

## What is a horizontal shrink by 1 2?

The horizontal shrink means you shrink x by a factor of 1/2. Currently the slope on the right side of the V is 1, so to “shrink” it, you actually DIVIDE by 1/2, giving you a new slope of 2.

## Why are horizontal stretches opposite?

Why are horizontal translations opposite? While translating a graph horizontally, it might occur that the procedure is opposite or counter-intuitive. That means: For negative horizontal translation, we shift the graph towards the positive x-axis.