Understanding Vertical Stretch in Mathematics: Exploring the Height-changing Transformation and its Effects

vertical stretch

In mathematics, a vertical stretch refers to a transformation that changes the height of a graph or an object

In mathematics, a vertical stretch refers to a transformation that changes the height of a graph or an object. It is a type of dilation where every point on a graph or in a shape is moved vertically away from or towards the x-axis.

To understand vertical stretch, let’s consider a simple linear function, such as y = 2x. By looking at the coefficients of the equation, we can see that the slope is 2. This means that for every unit increase in x, the value of y increases by 2. We can visualize this as a straight line on a coordinate plane.

Now, if we apply a vertical stretch to this function, we would multiply the entire equation by a constant greater than 1. For example, if we multiply the original equation by 3, we obtain y = 6x. The new equation represents a vertical stretch by a factor of 3, which means that for every unit increase in x, the value of y will increase by 6.

Graphically, a vertical stretch makes the graph of a function or the shape of an object taller or shorter. In the case of a linear function, the steepness of the line increases if the vertical stretch factor is greater than 1 or decreases if the factor is between 0 and 1. The x-intercept of the function remains unchanged, but the y-intercept may shift depending on the constant multiplied.

It is important to note that a vertical stretch affects the y-values of the points on a graph while keeping the x-values intact. This transformation can be applied to any type of function or geometric shape, not just linear equations.

In summary, a vertical stretch is a transformation that changes the height of a graph or object while maintaining its shape by multiplying the equation or coordinates by a constant greater than 1.

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