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.

Can a function be stretched by a factor of 3?

- To attain y = |x/
**3**|, we stretch the parent function y = |x|**by**a**factor of 3**. The graph shown above confirms this, and we can apply the same process**when**horizontally**stretching**the graphs**of**other functions. Ready to graph more functions and apply horizontal stretches?

Contents

- 1 What is a vertical stretch factor of 3?
- 2 What does stretch by a factor mean?
- 3 What is a horizontal stretch by a factor of 2?
- 4 How do you calculate stretch factor?
- 5 How do you stretch a horizontal by a factor of 3?
- 6 What is vertical stretch factor?
- 7 What is a vertical compression by a factor of 1 3?
- 8 What does stretching a graph mean?
- 9 How is a stretch different from a dilation?
- 10 What is a horizontal stretch?
- 11 How do you describe a horizontal stretch?
- 12 What does 2f A mean?

## What is a vertical stretch factor of 3?

Stretching f(x) vertically by a factor of 3 will result to h(x) being equal to 3 times f(x). Hence, h(x) = 3|x|.

## What does stretch by a factor mean?

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).

## What is a horizontal stretch by a factor of 2?

The graph of y=(0.5x)2 y = ( 0.5 x ) 2 is a horizontal stretch of the graph of the function y=x2 y = x 2 by a factor of 2. The graph of y=(2x)2 y = ( 2 x ) 2 is a horizontal compression of the graph of the function y=x2 y = x 2 by a factor of 2.

## How do you calculate stretch factor?

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 stretch a horizontal 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.

## What is vertical stretch factor?

The vertical stretch of a graph measures the stretching or shrinking factor in the vertical direction. For example, if a function increases three times as fast as its parent function, it has a stretch factor of 3. If the graph has a single vertex and a strictly increasing slope, it is most likely a parabola.

## What is a vertical compression by a factor of 1 3?

Say if you have an absolute value function f(x)= |4-x|, the way you would vertically compress it is by affecting it’s slope. If you multiply the number in front of x by 1 1/3 or 1.3333 repeating. The 1 aspect of 1 and 1/3 helps the slope stay constant, the 1/3 or. 3333 repeating compresses it vertically by 1/3.

## What does stretching a graph mean?

When we multiply a function by a positive constant, we get a function whose graph is stretched or compressed vertically in relation to the graph of the original function. If the constant is greater than 1, we get a vertical stretch; if the constant is between 0 and 1, we get a vertical compression.

## How is a stretch different from a dilation?

A reduction (think shrinking) is a dilation that creates a smaller image, and an enlargement (think stretch) is a dilation that creates a larger image. If the scale factor is between 0 and 1 the image is a reduction. If the scale factor is greater than 1, the image is an enlargement.

## 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 describe a horizontal stretch?

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 ).

## What does 2f A mean?

2f(a) is two times the value of f applied at a. For example, if f(x) = x^2, then f(2a) = (2a)^2 = 4a^2, and 2f(a) = 2a^2.