How do you vertically stretch a graph in math?

- Since B (x) = 2 ∙ A (x), we vertically stretch the graph of A (x) by a scale factor of 2. To do this, we can take note of some points from the graph and find their corresponding values for B (x). To find the new ordered pairs, let’s multiply each y-coordinate by 2. We can connect these points to form B (x).

Contents

- 1 What values stretch the graph vertically?
- 2 What happens to the coordinates when a graph is stretched vertically?
- 3 How do you graph a vertical stretch?
- 4 What does it mean to vertically stretch a graph?
- 5 How do you translate a graph vertically?
- 6 How do you identify transformations?
- 7 What does a vertical stretch affect?
- 8 What does vertically compressed mean?
- 9 How do you vertically stretch a linear function?
- 10 How do you do a vertical stretch and compression?
- 11 Is a vertical stretch negative or positive?
- 12 How is a stretch different from a dilation?
- 13 Which function represents a vertical stretch of an exponential function?

## What values stretch the graph 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 ).

## What happens to the coordinates when a graph is stretched vertically?

When a graph is stretched or shrunk vertically, the x -intercepts act as anchors and do not change under the transformation. if 0 < k < 1. Remember that x-intercepts do not move under vertical stretches and shrinks. In other words, if f (x) = 0 for some value of x, then k f (x) = 0 for the same value of x.

## How do you graph a vertical stretch?

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

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

## What does it mean to vertically stretch a graph?

A vertical stretching is the stretching of the graph away from the x-axis. 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.

## How do you translate a graph vertically?

Vertically translating a graph is equivalent to shifting the base graph up or down in the direction of the y-axis. A graph is translated k units vertically by moving each point on the graph k units vertically. g (x) = f (x) + k; can be sketched by shifting f (x) k units vertically.

## How do you identify transformations?

The function translation / transformation rules:

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

## What does a vertical stretch affect?

Vertical stretch occurs when a base graph is multiplied by a certain factor that is greater than 1. This results in the graph being pulled outward but retaining the input values (or x). When a function is vertically stretched, we expect its graph’s y values to be farther from the x-axis.

## What does vertically compressed mean?

Vertical compression means making the y-value smaller for any given value of x, and you can do it by multiplying the entire function by something less than 1. Horizontal stretching means making the x-value bigger for any given value of y, and you can do it by multiplying x by a fraction before any other operations.

## How do you vertically stretch a linear function?

How To: Given the equation of a linear function, use transformations to graph A linear function OF the form f(x)=mx+b

- Graph f(x)=x f ( x ) = x.
- Vertically stretch or compress the graph by a factor of |m|.
- Shift the graph up or down b units.

## 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

## Is a vertical stretch negative or positive?

When you multiply a function by a positive a you will be performing either a vertical compression or vertical stretching of the graph. If 0 < a < 1 you have a vertical compression and if a > 1 then you have a vertical stretching.

## 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.

## Which function represents a vertical stretch of an exponential function?

The correct answer is A. f(x)=3(1/2)^x.