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This page provides a list of educational videos related to Reflections and Graphs. You can also use this page to find sample questions, apps, worksheets, lessons , infographics and presentations related to Reflections and Graphs.

Reflections by Matrices

By Susan Loughry

This video explains how a matrix can reflect a shape on a graph.

Transformations of Functions

By The Organic Chemistry Tutor

This precalculus video tutorial provides a basic introduction into transformations of functions. It explains how to identify the parent functions as well as vertical shifts, horizontal shifts, vertical stretching and shrinking, horizontal stretches and compressions, reflection about the x-axis, reflection about the y-axis, reflections about the origins and more. Parent functions include absolute value functions, quadratic functions, cubic functions, and radical functions. This video contains plenty of examples on graphing functions using transformations.

Inverse Functions | MathHelp.com

By MathHelp.com

In this example, we’re given a relation in the form of a chart, and we’re asked to find the inverse of the relation, then graph the relation and its inverse. To find the inverse of a relation, we simply switch the x and y values in each point. In other words, the point (1, -4) becomes (-4, 1), the point (2, 0) becomes (0, 2), the point (3, 1) becomes (1, 3), and the point (6, -1) becomes (-1, 6). Next, we’re asked to graph the relation and its inverse, so let’s first graph the relation. Notice that the relation contains the points (1, -4,), (2, 0), (3, 1), and (6, -1). And the inverse of the relation contains the points (-4, 1), (0, 2), (1, 3), and (-1, 6). Finally, it’s important to understand the following relationship between the graph of a relation and its inverse. If we draw a diagonal line through the coordinate system, which is the line that has the equation y = x, notice that the relation and its inverse are mirror images of each other in this line. In other words, the inverse of a relation is the reflection of the original relation in the line y = x.

Inverse Relations | MathHelp.com

By MathHelp.com

Here we’re asked to solve for x in the equation: log base x of 144 = 2. Notice that we have a logarithmic equation, so let’s first convert the equation to exponential form. Remember that the base of the log represents the base of the power, the right side of the equation represents the exponent, and the number inside the log represents the result, so we have x…squared…= 144. Now, to solve for x, since x is squared, we simply take the square root of both sides of the equation to get x = plus or minus 12. Remember to always use plus or minus when taking the square root of both sides of an equation. However, notice that x represents the base of the logarithm in the original problem, and the base of a logarithm cannot be negative. Therefore, x cannot be equal to negative 12. So our final answer is x = 12.

Systems of Three Equations | MathHelp.com

By MathHelp.com

Here we’re asked to graph the following function and use the horizontal line test to determine if it has an inverse. And if so, find the inverse function and graph it. So let’s start by graphing the given function, f(x) = 2x – 4, and remember that f(x) is the same as y, so we can rewrite the function as y = 2x – 4. Now, we simply graph the line y = 2x – 4, which has a y-intercept of -4, and a slope of 2, or 2/1, so we go up 2 and over 1, plot a second point and graph our line, which we’ll call f(x). Next, we’re asked to use the horizontal line test to determine if the function has an inverse. Since there’s no way to draw a horizontal line that intersects more than one point on the function, the function does have an inverse. So we need to find the inverse and graph it. To find the inverse, we switch the x and the y in original function, y = 2x – 4, to get x = 2y – 4. Next, we solve for y, so we add 4 to both sides to get x + 4 = 2y, and divide both sides by 2 to get 1/2x + 2 = y. Next, let’s flip our equation so that y is on the left side, and we have y = 1/2x + 2. Finally, we replace y with the notation that we use for the inverse function of f, as shown here. And remember that we’re asked to graph the inverse as well, so we graph y = ½ x + 2. Our y-intercept is positive 2, and our slope is ½, so we go up one and over 2, plot a second point, graph the line, and label it as the inverse function of f. Notice that the graph of the inverse function is a reflection of the original function in the line y = x.

Recovering the Sequence of Transformations to Show Congruence or Similarity

By James Olsen

Directions: Two figures will be given. Determine if they are congruent or similar. Then state the sequence of transformations that exhibits the congruence or similarity. There is an error in this video!! In example 3, the first translation should be using vector BF (and not vector AF). This is aligned with the following Common Core State Standards for Mathematics: [8.G.2] Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. [8.G.4] Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two- dimensional figures, describe a sequence that exhibits the similarity between them. [G.CO.5] Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. [G.SRT.2] Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar

Land and Water: Crash Course Kids #16.1

By Crash Course Kids

8th Grade Math

By Lumos Learning

8th grade math lesson addressing Common Core Standards (Massachusetts Curriculum Framework Standard 8.EE.6).

8th Grade Math

By

8th grade math lesson addressing Common Core Standards (Massachusetts Curriculum Framework Standard 8.EE.6).

Water Water Everywhere: Crash Course Kids #14.2

By Crash Course Kids

12 - What are Inverse Functions? (Part 1) - Find the Inverse of a Function & Graph

By Math and Science

Quality Math And Science Videos that feature step-by-step example problems!

06 - Graphing Parabolas - Shifting Vertically (Quadratic Functions)

By Math and Science

Quality Math And Science Videos that feature step-by-step example problems!

Area Between Two Curves

By The Organic Chemistry Tutor

This calculus video tutorial provides a basic introduction in finding the area between two curves with respect to y and with respect to x. It explains how to set up the definite integral to calculate the area of the shaded region bounded by the two curves. In order to find the points of intersection, you need to set the two curves equal to each other and solve for x or y. You need to be familiar with some basic integration techniques for this lesson. This video contains plenty of examples and practice problems.

Writing Systems: Crash Course Linguistics #16

By Math and Science

Quality Math And Science Videos that feature step-by-step example problems!

16 - What do Imaginary & Complex Roots of Equations Mean?

By Math and Science

Quality Math And Science Videos that feature step-by-step example problems!

MAP 2020-21 Blueprint and Best Practices | 10 Min. webinar organized by EdShorts

By Lumos Learning

This Free 10 Min power-packed webinar organized by EdShorts on Jan 28th provides all the information available about 2021 LEAP Assessments - such as testing guidelines, blueprint changes, testing windows, and more! Join the EdShorts Facebook community today: https://www.facebook.com/groups/60370... for more bite-sized power-packed webinars every week!