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 factor a horizontal stretch?
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.
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.
How do you vertically compress by a factor of 1 2?
In general, when a function is compressed vertically by a (where 0 < a < 1), the graph shrinks by the same scale factor. Let’s apply the concept to compress f(x) = 6|x| + 8 by a scale factor of 1/2. To compress f(x), we’ll multiply the output value by 1/2.
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 do you stretch by a factor of 2?
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.
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.
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.
How do you stretch a graph by a factor of 1 2?
The graph of g(x)=12×2 g ( x ) = 1 2 x 2 is compressed vertically by a factor of 2; each point is half as far from the x -axis as its counterpart on the graph of y=x2. y = x 2 . In general, we have the following principles….SectionVertical Stretches and Compressions.
| x | y=x2 | f(x)=2×2 |
|---|---|---|
| −2 | 4 | 8 |
| −1 | 1 | 2 |
| 0 | 0 | 0 |
| 1 | 1 | 2 |
How do you stretch a function vertically by 2?
What is horizontal stretch and shrink?
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.
What is vertical stretch or shrink?
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.
What is a vertical stretch?
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.
What is a horizontal stretch of a function?
A horizontal stretching is the stretching of the graph away from the y-axis. When a function is horizontally stretched by a factor, k, the x-value of the function is multiplied by the factor k.
What is a horizontal stretch transformation?
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). Examples of Horizontal Stretches and Shrinks.