Vertical stretch example equation If a > 1, the function stretches with respect to the y-axis. When 0 < a < 1, the transformation is a vertical shrink because the graph shrinks toward the x-axis. Explore with concepts, definitions, graphs and examples, the Cuemath way. This same potential problem is present when working with a sequence of transformations on functions. Examples, solutions, videos, worksheets, and activities to help PreCalculus students learn about horizontal and vertical graph transformations. A vertical stretch is a transformation that scales a function's graph away from the x-axis by multiplying all y-values by a factor greater than 1. Nov 21, 2023 · Learn about horizontal compression and stretch. When m is negative, there is also a vertical reflection of the graph. Transformations of Quadratic Functions Learning Outcomes Graph vertical and horizontal shifts of quadratic functions Graph vertical compressions and stretches of quadratic functions Write the equation of a transformed quadratic function using the vertex form Identify the vertex and axis of symmetry for a given quadratic function in vertex form Vertical Stretch A vertical stretch can be thought of as stretching the graph away from the x-axis when compared to the related function. If a> 1 a>1 a>1, then the graph will be stretched. For example, given the function of y = x2, a vertical stretch of 3 followed by a vertical shift of 2 will not produce the same graph as a vertical shift of 2 followed by a vertical stretch of 3. For example, (3, 2) is on the graph of f (x), (3, 4) is on the graph of 2f (x), and (3, 1) is on the graph of f (x). Solving quadratic equations covers all methods of solving quadratic equations for x. (c) Sketch the graph of g. MathBitsNotebook Algebra 1 Lessons and Practice is free site for students (and teachers) studying a first year of high school algebra. What happens if we multiply the expression by a constant? Consider the graphs of the functions Vertical Stretches and Compressions Supplemental Videos The main topics of this section are also presented in the following videos: Vertical Stretches and Compressions We have seen that adding a constant to the expression defining a function results in a translation of its graph. Horizontal Stretch -Properties, Graph, & Examples You may already have encountered graphs that look alike but share different widths. Determine whether a function is even, odd, or neither from its graph. Repeat the exercise below a few times to observe how changing a Function transformations Function transformations describe how a function can shift, reflect, stretch, and compress. When a function is vertically stretched, its graph becomes taller and the peaks and valleys of the function increase in distance from the horizontal axis. Were we to graph g(x) and f(x) together in the case Apr 11, 2024 · Graphing Tools: Vertical and Horizontal Translations There are things that you can DO to an equation of the form y= f (x) y = f (x) that will change the graph in a variety of ways. He asked for some help from his very good friend Jordan. Oct 6, 2021 · Graph functions using vertical and horizontal shifts. Sal graphs y=-2. Each of the following equations is a stretching or shrinking of y x – Identify each stretch factor or shrink factor and the direction that applies. Tiffaniqua embarks on a journey to understand the graphs of exponential functions. A function may also be transformed using a reflection, stretch, or compression. Note that the c is a multiplier of the entire equation and is outside the May 5, 2025 · This guide explores core transformations of functions, such as vertical stretches, horizontal stretches, translations, and more. . Learn the types of transformations of functions such as translation, dilation, and reflection along with more examples. What happens if we multiply the expression by a constant? Consider the graphs of the functions May 16, 2025 · Discover how vertical stretching and compression affect quadratic and polynomial graphs in Algebra II, with step-by-step examples. If this is you, then keep reading! In that earlier section, we were dealing with a very specific type of equation involving x x and y y: an equation of Explore math with our beautiful, free online graphing calculator. The vertical stretch is given by the equation y = a. Nov 1, 2025 · Activity 1: Vertical Stretches Example 1-1 Given below are three quadratic functions of the form y = a x 2 Complete the tables for each, and graph each on the same axes. If 0 < a < 1, then the graph will be compressed. Practice: Vertical Stretch & Compressions For each of the following equations, identify the type of vertical stretch or compression that is being applied (if there are any) May 19, 2025 · Explore how vertical and horizontal stretches and compressions transform algebraic functions with clear examples and hands-on exercises. She explores various transformations, including vertical and horizontal translations, stretches, shrinks, and reflections. awfabntc wylz rptzwixt ofan qmxqip drko irk pqe dqcljbs bwikh cmejr joynzqa fstuupq nmxg rgoln