![]() A vertical reflection reflects a graph vertically across the x x -axis, while a horizontal. Another transformation that can be applied to a function is a reflection over the x x or y y -axis. Determine whether a function is even, odd, or neither from its graph. The product of their slopes is –1 making them perpendicular. Given a function f(x), a new function g(x) f(x) + k, where k is a constant, is a vertical shift of the function f(x). Graph functions using reflections about the x x -axis and the y y -axis. Aut(Cn) The cycle graph Cn can be represented as the 1-skeleton of a regular n-gon in the plane, as. In Example 3, verify that FF is perpendicular to y = –x. SOLUTIONĥ GUIDED PRACTICE for Examples 2 and 3 5. Reflect ABC in the lines y = –x and y = x. SOLUTION Use the coordinate rule for reflecting in y = –x. ![]() reflection reflects a graph horizontally across the y-axis. Then move 0.5 units right and 0.5 units down to locate G′ (2, 1).ģ EXAMPLE 3 Graph a reflection in y = –x Reflect FG from Example 2 in the line y = –x. A reflection is an example of a transformation that takes a shape (called the. From G, move 0.5 units right and 0.5 units down to y = x. From that point, move 1.5 units right and 1.5 units down to locate F′(2,–1). From F, move 1.5 units right and 1.5 units down to y = x. The following properties of reflections would be much useful for you to reflect a figure across a line of reflection. Each point and itsimage must be at the same distance from the line of reflection. Thenconnect the vertices to form the image. The segment from F to its image, FF ′, is perpendicular to the line of reflection y = x, so the slope of FF ′ will be –1 (because 1(–1) = –1). To reflect a figure across a line of reflection, reflect each of its vertices. Graph the segment and its image.Ģ EXAMPLE 2 Graph a reflection in y = x SOLUTION The slope of y = x is 1. Transformations are used to change the graph of a parent function into the graph of a more complex function.Presentation on theme: "EXAMPLE 2 Graph a reflection in y = x"- Presentation transcript:ġ EXAMPLE 2 Graph a reflection in y = x The endpoints of FG are F(–1, 2) and G(1, 2). Stretching a graph means to make the graph narrower or wider. They are caused by differing signs between parent and child functions.Ī shift, also known as a translation or a slide, is a transformation applied to the graph of a function that does not change the shape or orientation of the graph, only the location of the graph.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. The term is most commonly used for polynomial functions with a degree of at least three.Ī power function is a polynomial of the form f(x)=ax n where a is a real number and n is an integer with n≥1. All other functions of this type are usually compared to the parent function.Ī polynomial is an expression with at least one algebraic term, but which does not indicate division by a variable or contain variables with fractional exponents.Ī polynomial graph is the graph of a polynomial function. Reflection Over X-Axis & Y-Axis Equations, Examples & Graph Transformations. As x→∞,f(x)→∞, and as x→−∞,f(x)→−∞.Īs with quadratics and polynomials, the leading coefficient a changes the vertical “ stretching” of power functions.Ī stretch or compression is a function transformation that makes a graph narrower or wider, without translating it horizontally or vertically.Īn odd power function is a polynomial of the form f(x)=ax n where a is a real number and n is an odd integer.Ī parent function is the simplest form of a particular type of function. For example, when point P with coordinates (5,4) is reflecting across the Y. For odd powers n, the power function goes from the third quadrant to the first quadrant (like the line y=x).For even powers n, the power function f(x)=ax n is U-shaped (like a parabola) and as x→∞,f(x)→∞.The end behavior of a function describes the y−values as x gets very large (x→∞ in symbols) or as x gets very small (x→−∞). Notice that each power function has only one x− and y−intercept, the origin (0, 0). If n is even, then the power function is also called “even,” and if n is odd, then the power function is “odd.” The graphs of the first five power functions are shown below. A power function is a polynomial of the form f(x)=ax n where a is a real number and n is an integer with n≥1. The most simple polynomial is called a power function. All three these functions belong to a larger group of functions called the polynomial functions. ![]() You have already studied many different kinds of functions, for example linear functions, constant functions, and quadratic functions.
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