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.
How to vertically compress a graph?
Vertically compressed graphs take the same x-values as the original function and map them to smaller y-values, and vertically stretched graphs map those x-values to larger y-values.
How do you stretch and shrink a graph?
how do you stretch and shrink a graph? Stretches and Shrinks. 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. 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 ).
How to stretching and shrinking a graph?
- Y= Cos (2x)
- Y=-4Sin (x)
- Y= Sin (x/3 )
- Y= (1/4) Cos (x)
What is a horizontal stretch on a graph?
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. Learning how we can stretch graphs horizontally can help us understand the family of functions’ graphs.
How do you know if a graph is stretched vertically or horizontally?
3:165:17Ex: Identify Horizontal and Vertical Stretches and CompressionsYouTubeStart of suggested clipEnd of suggested clipCompressed function and because we multiply each x coordinate by one half we're going to say thatMoreCompressed function and because we multiply each x coordinate by one half we're going to say that the graph is horizontally compressed by a factor of one over b or in this case one half.
What does it mean to vertically stretch a graph?
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.
How do you tell if an equation is a vertical stretch or shrink?
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 describe a vertical stretch?
1:508:16Describing a transformation with vertical and horizontal stretch then ...YouTubeStart of suggested clipEnd of suggested clipYou know that now if I'm multiplying it by a number if it's if that number is greater than 1 it'sMoreYou know that now if I'm multiplying it by a number if it's if that number is greater than 1 it's going to be a vertical stretch.
What does a vertical stretch look like in an equation?
0:219:32Function Transformations: Horizontal and Vertical Stretches ... - YouTubeYouTubeStart of suggested clipEnd of suggested clipSo if we have y equals a times f of x where a is greater than one this will stretch the graph of fMoreSo if we have y equals a times f of x where a is greater than one this will stretch the graph of f of x vertically by a factor of a.
What causes a vertical stretch?
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.
How do you tell if a graph shrinks or stretches?
0:297:57Pre-Calculus - Applying stretching and shrinking transformations - YouTubeYouTubeStart of suggested clipEnd of suggested clipIf you multiply on the outside by a number between zero and one then it will shrink it. When you tryMoreIf you multiply on the outside by a number between zero and one then it will shrink it. When you try and do these same things to the inside of the function.
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.
How do you stretch vertically by a factor of 2?
0:025:00Vertical Stretch by a Factor of 2 Explained - YouTubeYouTubeStart of suggested clipEnd of suggested clipBut notice that the 2 is multiplying the Y values. The x squared gives you the Y value right so theMoreBut notice that the 2 is multiplying the Y values. The x squared gives you the Y value right so the 2 is multiplying those to get you new Y values.
How do you find the vertical stretch of a parabola?
0:062:37equations of parabolas finding stretch factor - YouTubeYouTubeStart of suggested clipEnd of suggested clipAnd one other point on the parabola. So the important thing here is you need to know the vertex. AndMoreAnd one other point on the parabola. So the important thing here is you need to know the vertex. And you need to know one other point.
Does a vertical stretch get wider?
A function that is vertically stretched has bigger y-values for any given value of x, and a function that is vertically compressed has smaller y-values for any given value of x. For example, look at the graph of a stretched and compressed function.
What is a horizontal stretch on a graph?
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.
Function Transformations: Horizontal And Vertical Translations
This video explains to graph graph horizontal and vertical translation in the form af (b (x-c))+d. It looks at how c and d affect the graph of f (x).
Function Transformations: Horizontal And Vertical Stretch And Compression
This video explains to graph graph horizontal and vertical stretches and compressions in the form af (b (x-c))+d. It looks at how a and b affect the graph of f (x).
Horizontal And Vertical Graph Stretches And Compressions (Part 2)
This video discusses the horizontal stretching and compressing of graphs.
Graph Transformations About The X-Axis And Y-Axis
This video talks about reflections around the X axis and Y axis. (Part 3)
Different Types Of Math Transformation
There are different types of math transformation, one of which is the type y = f (bx). This type of math transformation is a horizontal compression when b is greater than one. We can graph this math transformation by using tables to transform the original elementary function.
