We can also stretch and shrink the graph of a function. To stretch or shrink the graph in the y direction, multiply or divide the output by a constant. To stretch or shrink the graph in the x direction, divide or multiply the input by a constant.
- 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.
Contents
- 1 What is shrinking and stretching?
- 2 How do you tell if a function is shrinking or stretching?
- 3 What does stretching mean in algebra?
- 4 What is vertical stretch or shrink?
- 5 How do horizontal stretches and shrinks work?
- 6 What is a compression in math?
- 7 How do you compress and stretch a function?
- 8 How do you vertically shrink a graph?
- 9 How do you vertically stretch a graph?
- 10 How do you stretch and shrink a graph?
- 11 What are stretches in geometry?
- 12 What is stretch or compression in math?
- 13 Why are horizontal stretches opposite?
- 14 How do you shrink an absolute value graph?
What is shrinking and stretching?
While translations move the x and y intercepts of a base graph, stretches and shrinks effectively pull the base graph outward or compress the base graph inward, changing the overall dimensions of the base graph without altering its shape.
How do you tell if a function is shrinking or stretching?
If c is greater than one the function will undergo horizontal shrinking, and if c is less than one the function will undergo horizontal stretching. Horizontal scaling: The function y=sin(x) is shrunk by a factor of three in the x direction.
What does stretching mean in algebra?
stretch. A stretch or compression is a function transformation that makes a graph narrower or wider. stretching. Stretching a graph means to make the graph narrower or wider.
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.
How do horizontal stretches and shrinks work?
What are Horizontal Stretches and Shrinks? Horizontal stretches and shrinks, respectively, horizontally pull the base graph, or push it together, while leaving the y-intercept unchanged to anchor the graph.
What is a compression in math?
A compression occurs when a mathematical object is scaled by a scale factor less in absolute value than one. When a compression occurs, the image is smaller than the original mathematical object. If the scaling occurs about a point, the transformation is called a dilation and the “point” is called the dilation centre.
How do you compress and stretch a function?
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
How do you vertically shrink a graph?
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.
How do you vertically stretch a graph?
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 do you stretch and shrink a graph?
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 are stretches in geometry?
The image of a dilation is the same shape as the original figure, but is not necessarily the same size. If a figure is enlarged (or reduced) in only one direction, the change is referred to as a stretch. In a stretch, the figure is distorted, and is not necessarily similar to the original figure.
What is stretch or compression in math?
In math terms, you can stretch or compress a function horizontally by multiplying x by some number before any other operations. To stretch the function, multiply by a fraction between 0 and 1. To compress the function, multiply by some number greater than 1.
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 shrink an absolute value graph?
The stretching or compressing of the absolute value function y=| x | is defined by the function y=a| x | where a is a constant. The graph opens up if a>0 and opens down when a<0.