horizontal stretch by a factor of 2

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 write stretched by a factor of 2?

Thus, the equation of a function stretched vertically by a factor of 2 and then shifted 3 units up is y = 2f (x) + 3, and the equation of a function stretched horizontally by a factor of 2 and then shifted 3 units right is y = f ( (x – 3)) = f ( x – ). Example: f (x) = 2×2.

How do you stretch a horizontal function?

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 ) . In general, a horizontal stretch is given by the equation y=f(cx) y = f ( c x ) .

What is a horizontal stretch by a factor of 1 2?

When we horizontally stretch g(x) by a scale factor of 1/2, we obtain h(x). Let’s start with g(x). We can horizontally stretch f(x) to obtain g(x), so we divide the input value of f(x) by 5 to obtain g(x)’s expression: f(x/5). This means that in terms of f(x), g(x) = f(x/5) and h(x)= f(x/10).

What does vertically stretched by a factor of 2 mean?

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). Hence, h(x) = 3|x|.

What is a vertical compression by a factor of 2?

The graph of g(x)=12×2 g ( x ) = 1 2 x 2 is compressed vertically by a factor of 2; each point is half as far from the x -axis as its counterpart on the graph of y=x2.

How do you find horizontal stretch or compression?

If the constant is between 0 and 1, we get a horizontal stretch; if the constant is greater than 1, we get a horizontal compression of the function. Given a function y=f(x) y = f ( x ) , the form y=f(bx) y = f ( b x ) results in a horizontal stretch or compression.

How do you calculate stretch factor?

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.

Is horizontal stretch Same as vertical compression?

stretch is a transformation that results in the distance from the x-axis every point growing by a scale factor greater than 1 and a vertical compression is a transformation that results in the distance from the x-axis of every point shrinking by a scale factor between 0 and 1.

What is a horizontal stretch in math?

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.

How do you shrink a vertical BY 1 2?

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 stretch a function?

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.

Why is horizontal stretch 1 K?

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). Consider the following base functions, (1) f (x) = x2 – 3, (2) g(x) = cos (x).

How do you write a horizontal shrink of 1 2?

The horizontal shrink means you shrink x by a factor of 1/2. Currently the slope on the right side of the V is 1, so to “shrink” it, you actually DIVIDE by 1/2, giving you a new slope of 2. So now our function is y=|2x|. Which axis goes “up and down”: x or y?

What does f2 mean?

f(2) means that we should find the value of our function when x equals 2. Example. f(x)=x+7.