What makes a horizontal stretch

Grades 11 , Date Created:. Last Modified:. Function function family graph 8 more parent function reflect reflecting Reflection stretch stretching transform transformations. Language English. Concept Nodes: MAT. Show Hide Resources. Please wait Make Public. Upload Failed. To use this website, please enable javascript in your browser. In algebra, this essentially manifests as a vertical or horizontal shift of a function.

A translation can be interpreted as shifting the origin of the coordinate system. To translate a function vertically is to shift the function up or down. In general, a vertical translation is given by the equation:. The original function we will use is:. To translate a function horizontally is the shift the function left or right.

While vertical shifts are caused by adding or subtracting a value outside of the function parameters, horizontal shifts are caused by adding or subtracting a value inside the function parameters.

The general equation for a horizontal shift is given by:. Again, the original function is:. Reflections produce a mirror image of a function. As an example, let the original function be:. Consider an example where the original function is:. The third type of reflection is a reflection across a line. In algebra, equations can undergo scaling, meaning they can be stretched horizontally or vertically along an axis.

In general, the equation for vertical scaling is:. If we want to vertically stretch the function by a factor of three, then the new function becomes:. Adding a constant to the inputs or outputs of a function changed the position of a graph with respect to the axes, but it did not affect the shape of a graph. We now explore the effects of multiplying the inputs or outputs by some quantity. We can transform the inside input values of a function or we can transform the outside output values of a function.

Each change has a specific effect that can be seen graphically. 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. The graph below shows a function multiplied by constant factors 2 and 0. Sketch a graph of this population.

If we choose four reference points, 0, 1 , 3, 3 , 6, 2 and 7, 0 we will multiply all of the outputs by 2. Notice that the effect on the graph is a vertical stretching of the graph, where every point doubles its distance from the horizontal axis. Each output value is divided in half, so the graph is half the original height. When trying to determine a vertical stretch or shift, it is helpful to look for a point on the graph that is relatively clear. Write the formula for the function that we get when we vertically stretch or scale the identity toolkit function by a factor of 3, and then shift it down by 2 units.