What Is A Vertical Stretch Example?

What is a vertical stretch by a factor of 2?

Stretching f(x) vertically by a factor of 2 will result in h(x) being equal to 2 times f(x).

Stretching f(x) vertically by a factor of 3 will result to h(x) being equal to 3 times f(x)..

What does a vertical stretch look like on 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 do a vertical stretch by a factor of 3?

If g(x) = 3f (x): For any given input, the output iof g is three times the output of f, so the graph is stretched vertically by a factor of 3. If g(x) = f (3x): For any given output, the input of g is one-third the input of f, so the graph is shrunk horizontally by a factor of 3.

What is a vertical shift?

Vertical shifts are outside changes that affect the output ( y- ) axis values and shift the function up or down. … Combining the two types of shifts will cause the graph of a function to shift up or down and right or left.

How do you find a vertical asymptote?

Vertical asymptotes can be found by solving the equation n(x) = 0 where n(x) is the denominator of the function ( note: this only applies if the numerator t(x) is not zero for the same x value). Find the asymptotes for the function . The graph has a vertical asymptote with the equation x = 1.

What does a vertical stretch affect?

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 its a vertical stretch or shrink?

Key Points When by either f(x) or x is multiplied by a number, functions can “stretch” or “shrink” vertically or horizontally, respectively, when graphed. In general, a vertical stretch is given by the equation y=bf(x) y = b f ( x ) .

What is a vertical and horizontal stretch?

vertical stretching/shrinking changes the y -values of points; transformations that affect the y -values are intuitive. horizontal stretching/shrinking changes the x -values of points; transformations that affect the x -values are counter-intuitive.

How do you find vertical translation?

Vertically translating a graph is equivalent to shifting the base graph up or down in the direction of the y-axis. A graph is translated k units vertically by moving each point on the graph k units vertically. g (x) = f (x) + k; can be sketched by shifting f (x) k units vertically.

How do you find the vertical stretch of a rational function?

Given a simple rational function, f, and a new function g such that , then: Ø If , then the graph of g is a vertical stretch of the graph of f by a factor of c. Ø If , then the graph of g is a vertical compression of the graph of f by a factor of c.

What is a stretch in math?

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. Horizontal Stretch. (“Horizontal Dilation”)

How do you know if a function is even or odd?

You may be asked to “determine algebraically” whether a function is even or odd. To do this, you take the function and plug –x in for x, and then simplify. If you end up with the exact same function that you started with (that is, if f (–x) = f (x), so all of the signs are the same), then the function is even.

What is a vertical stretch?

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.