What is horizontal stretch and shrink?
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.
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. Understanding the common parent functions we might encounter.
What is a stretch and shrink of graphs?
What are Vertical Stretches and Shrinks? 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 know if a graph is a horizontal stretch or shrink?
If b>1 , the graph stretches with respect to the y -axis, or vertically. If b<1 , the graph shrinks with respect to the y -axis. In general, a horizontal stretch is given by the equation y=f(cx) y = f ( c x ) .
How do you shrink horizontally?
To shrink or compress horizontally by a factor of c, replace y = f(x) with y = f(cx). Note that if |c|<1, that’s the same as scaling, or stretching, by a factor of 1/c.
How do you find stretch or shrink?
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.
How do you describe a horizontal stretch?
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).
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 does a horizontal shrink do?
Is a vertical shrink the same as a horizontal stretch?
With a parabola whose vertex is at the origin, a horizontal stretch and a vertical compression look the same.
How do you find the stretch factor of a graph?
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 does stretching and shrinking affect a graph?
Vertical/Horizontal Stretching/Shrinking usually changes the shape of a graph. Need a short break? gives a thorough discussion of horizontal and vertical stretching and shrinking. The key concepts are repeated here. The exercises in this lesson duplicate those in Graphing Tools: Vertical and Horizontal Scaling .
How to calculate horizontal and vertical graph stretches?
Horizontal And Vertical Graph Stretches And Compressions (Part 1) The general formula is given as well as a few concrete examples. y = c f(x), vertical stretch, factor of c; y = (1/c)f(x), compress vertically, factor of c; y = f(cx), compress horizontally, factor of c; y = f(x/c), stretch horizontally, factor of c; y = – f(x), reflect at x-axis
When does a vertical shrinking occur in a function?
Graphically, a vertical shrinking pulls the graph of toward the x-axis. When in the function , a vertical stretching of the graph of will occur. A vertical stretching pushes the graph of away from the x-axis.
What is the definition of a horizontal stretch?
This is called a horizontal stretch. A point (a,b) (a, b) on the graph of y= f(x) y = f (x) moves to a point (ka,b) (k a, b) on the graph of y =f(x k) y = f (x k). This transformation type is formally called horizontal scaling (stretching/shrinking).
