How do you stretch vertically?

Key Takeaways

1. When by either f(x) or x is multiplied by a number, functions can “stretch” or “shrink” vertically or horizontally, respectively, when graphed.
2. In general, a vertical stretch is given by the equation y=bf(x) y = b f ( x ) . …
3. In general, a horizontal stretch is given by the equation y=f(cx) y = f ( c x ) .

What does it mean to be stretched vertically?

What is 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 stretch 3 vertically?

Video quote: If you take that real number and multiply it times your original function you're going to get a vertical stretch. If that real if the absolute value of that real number is greater than 1.

What makes a function stretch vertically?

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.

What is a vertical stretch example?

Examples of Vertical Stretches and Shrinks



looks like? Using the definition of f (x), we can write y₁(x) as, y₁ (x) = 1/2f (x) = 1/2 ( x² – 2) = 1/2 x² – 1. Based on the definition of vertical shrink, the graph of y₁(x) should look like the graph of f (x), vertically shrunk by a factor of 1/2.

How do you do a vertical stretch and compression?

Video quote: I will have a vertical stretch or a vertical compression involved if a is greater than 1 that is a vertical stretch if a is between 0 & 1 the graph is flattened out that is a vertical compression.

What is horizontal stretching?

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 you stretch a function vertically by 2?

Video quote: The x squared gives you the Y value right so the 2 is multiplying those to get you new Y values. And notice too that every Y value doubled.

How do you stretch horizontal and vertical graphs?

Video quote: Function. So if we have y equals a times f of X where a is greater than 1 this will stretch the graph of f of X vertically by a factor of a.

How do you know if it is a horizontal or vertical stretch?

Video quote: And then if a is between zero. And one for example if a is 1/2 or 0.5. Notice how the graph of y equals 0.5. Times f of X is what's called a vertical compression.

How do you find the horizontal stretch?

Video quote: And if a is between 0 1 1 we have a vertical compression. Which we see here by y equals 0.5 times f of X. But again in our case because we have a horizontal stretch. We're concerned about find the