Transformations are used to change the graph of a parent function into the graph of a more complex function. Stretching a graph means to make the graph narrower or wider. They are caused by differing signs between parent and child functions.Ī stretch or compression is a function transformation that makes a graph narrower or wider. Reflections are transformations that result in a "mirror image" of a parent function. For each of my examples above, the reflections in either the x- or y-axis produced a graph that was. We really should mention even and odd functions before leaving this topic. Reflecting a graph means to transform the graph in order to produce a "mirror image" of the original graph by flipping it across a line. Reflection in y-axis (green): f(x) x 3 3x 2 x 2. All other functions of this type are usually compared to the parent function. Sketch the graph of each of the following transformations of y = xĪ stretch or compression is a function transformation that makes a graph narrower or wider, without translating it horizontally or vertically.įunction families are groups of functions with similarities that make them easier to graph when you are familiar with the parent function, the most basic example of the form.Ī parent function is the simplest form of a particular type of function. Graph each of the following transformations of y=f(x). Let y=f(x) be the function defined by the line segment connecting the points (-1, 4) and (2, 5). Notice that if we first reflect the object in QI around the (y)-axis and then follow that with a reflection around the (x)-axis, we get an image in QIII. We recommend using aĪuthors: Paul Peter Urone, Roger Hinrichs For example, in Figure 1.5.5 the original object is in QI, its reflection around the (y)-axis is in QII, and its reflection around the (x)-axis is in QIV. Use the information below to generate a citation. Then you must include on every digital page view the following attribution: If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: The center is put on a graph where the x axis and y axis cross, so we get this neat. If you are redistributing all or part of this book in a print format, reflection across the y-axis 1) 1 Geometry Unit 1 Practice Test. Changes were made to the original material, including updates to art, structure, and other content updates. Want to cite, share, or modify this book? This book uses theĪnd you must attribute Texas Education Agency (TEA). To do this, we separate projectile motion into the two components of its motion, one along the horizontal axis and the other along the vertical. Since vertical and horizontal motions are independent, we can analyze them separately, along perpendicular axes. Keep in mind that if the cannon launched the ball with any vertical component to the velocity, the vertical displacements would not line up perfectly. The graph of ykx is the graph of yx scaled by a factor of k. You can see that the cannonball in free fall falls at the same rate as the cannonball in projectile motion. Scaling & reflecting absolute value functions: equation. Figure 5.27 compares a cannonball in free fall (in blue) to a cannonball launched horizontally in projectile motion (in red). When the negative sign is on the outside, it reflects over the x-axis. Reflection Over X-Axis and has initial value of 1. When the multiplier is less than 1, then it horizontally shinks. The most important concept in projectile motion is that when air resistance is ignored, horizontal and vertical motions are independent, meaning that they don’t influence one another. When the multiplier is less than 1, it horizontally stretches. Ask students to guess what the motion of a projectile might depend on? Is the initial velocity important? Is the angle important? How will these things affect its height and the distance it covers? Introduce the concept of air resistance. Review addition of vectors graphically and analytically.
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