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.
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- 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.
Contents
- 1 How do you stretch a graph?
- 2 How do you tell if a graph is a stretch or shrink?
- 3 What does it mean to stretch a graph horizontally?
- 4 What does stretching mean in math?
- 5 What does 2f A mean?
- 6 What is a stretch and shrink of graphs?
- 7 How do you find the stretch factor of a graph?
- 8 What is a vertical stretch on a graph?
- 9 How is a stretch different from a dilation?
- 10 What is the difference between a horizontal and vertical stretch?
- 11 Why are horizontal stretches opposite?
- 12 What does enlargement mean in geometry?
- 13 What does a do to a graph?
- 14 What is stretch or compression in math?
How do you stretch a graph?
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 do you tell if a graph is a 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 ).
What does it mean to stretch a graph horizontally?
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).
What does stretching mean in math?
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 does 2f A mean?
2f(a) is two times the value of f applied at a. For example, if f(x) = x^2, then f(2a) = (2a)^2 = 4a^2, and 2f(a) = 2a^2.
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 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.
What is a vertical stretch on 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 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.
What is the difference between a horizontal and vertical stretch?
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. A horizontal compression (or shrinking) is the squeezing of the graph toward the y-axis.
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.
What does enlargement mean in geometry?
Enlarging a shape changes its size. A transformation is a way of changing the size or position of a shape. To enlarge a shape, a centre of enlargement is required. When a shape is enlarged from a centre of enlargement, the distances from the centre to each point are multiplied by the scale factor.
What does a do to a graph?
This is the most basic graph of the function. But transformations can be applied to it, too. It can be written in the format shown to the below. In this format, the “a” is a vertical multiplier and the “b” is a horizontal multiplier.
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.