What Does Stretching By 2 Mean? (Solved)

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.

What happens when you stretch f ( x ) by 3?

• 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|. Observe the two functions shown below and relate h (x) to g (x).

What does stretch 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).

How do you write a horizontal stretch 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 – ).

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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 calculate stretch factor?

1. Refer to: y=af(b(x−h))+k.
2. A vertical stretch is the stretching of a function on the x-axis.
3. A horizontal stretch is the stretching of a function on the y-axis.
4. For example:
5. b=12.
6. To vertically stretch we use this formula:
7. To horizontally stretch we use this formula:
8. x1=x12.

How do you tell if it is a vertical stretch or shrink?

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 vertical stretch mean?

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 vertical stretch factor?

The vertical stretch of a graph measures the stretching or shrinking factor in the vertical direction. For example, if a function increases three times as fast as its parent function, it has a stretch factor of 3. If the graph has a single vertex and a strictly increasing slope, it is most likely a parabola.

Is a vertical stretch negative or positive?

When you multiply a function by a positive a you will be performing either a vertical compression or vertical stretching of the graph. If 0 < a < 1 you have a vertical compression and if a > 1 then you have a vertical stretching.

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What does horizontal stretch mean?

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 horizontal stretch?

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 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).

What is a vertical compression of 1 3?

Say if you have an absolute value function f(x)= |4-x|, the way you would vertically compress it is by affecting it’s slope. If you multiply the number in front of x by 1 1/3 or 1.3333 repeating. The 1 aspect of 1 and 1/3 helps the slope stay constant, the 1/3 or. 3333 repeating compresses it vertically by 1/3.

What is a vertical compression by a factor of 2 3?

(1) A vertical compression of 2/3 is achieved by multiplying the function by 2/3. This reduces the amplitude by a factor of 2/3. Thus the leading coefficient is 2/3. (2) A reflection in the x-axis is achieved by multiplying f(x) by -1.