Figure 23 Given a function y f ( x ), y f ( x ), the form y f ( b x ) y f ( b x ) results in a horizontal stretch or compression. Quadratic Functions could also be shown with a b value, however since a parabola has horizontal symmetry it is usually not included.Ĭlick on the buttons below for more details on each transformation. 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. If by any chance the graph of g(x) was to be graphed on the basic of the parent function then, yes, all of the characteristics of the graph needs to be in mind. horizontal stretch or compression is the reciprocal of the stretch or compression. Thus he ignored the rest part of the equation since that was not required for graphing. Graph of the horizontal reflection of the square root function. If the value of b is negative the function is reflected across the y-axis. The only change is that g(x) is a horizontal stretch by a factor of 2 than f(x). A horizontal compression will give the same outcome as a vertical stretch (by the same factor), and a horizontal stretch produces the same outcome as a vertical compression. A horizontal compression pushes the graph closer to the y-axis, while a horizontal stretch pulls them away from the y-axis. The b value controls the horizontal stretch or horizontal compression. The quadratic graph is f(x) x 2, whereas the square-root graph is g(x) x 1/2. A square-root graph is related to a quadratic graph. Horizontal Compressions and Stretches (b) This figure shows an example of a quadratic function in graph form. Notice from the diagram on the right, the a, h, and k values preform the same transformations as they did in the quadratic function. Recall that the parent function of a quadratic is y = x^2 and the transformations applied to this parent function in h,k form, is what determines the parabola after the transformations. To the right you see the point of origin is (0, 0). This is why the square root function has a point of origin (starting point). Other important transformations include vertical shifts, horizontal shifts, and reflections. This is because taking the square root of a negative number results in a non-real number. Notice there are no negative x values in the parent function. The graph and table of the parent function is show to the right. A Square root function contains a square root with the independent variable (x) under the radical. Square root functions can also be written in h,k form.

Horizontal compression square root