So the image (that is, point B) is the point (1/25, 232/25). The most common lines of reflection are the x-axis, the y-axis. We can also represent Reflection in the form of matrix -. By examining the coordinates of the reflected image, you can determine the line of reflection. We can represent the Reflection along x-axis by following equation. Reflection along X-axis: In this kind of Reflection, the value of X is positive, and the value of Y is negative. So the intersection of the two lines is the point C(51/50, 457/50). Now we need to find the intersection of the lines y = 7x + 2 and y = (-1/7)x + 65/7 by solving this system of equations. Step 1 : Since we do reflection transformation across the y-axis, we have to replace x by -x in the given function y x Step 2 : So, the formula that. So the equation of this line is y = (-1/7)x + 65/7. y f(-x) is the reflection of y f(x) with resepct to the y-axis. We know that the slope of any line parallel to x-axis is 0. a A reflection in the y - axis and a stretch. (i) Substituting x 1 and y 3 in the given equation, we have. Here, y - f(x) is the reflection of y f(x) with respect to the x-axis. 1 Exercise 4.2B Reasoning and problem - solving Give the equation of the line of. Multiply all inputs by 1 for a horizontal reflection. The new graph is a reflection of the original graph about the x-axis. This occurs whenever we see the multiplication of a minus sign happening somewhere in the function. Multiply all outputs by 1 for a vertical reflection. Substituting the point (2,9) givesĩ = (-1/7)(2) + b which gives b = 65/7. A reflection of a function is just the image of the curve with respect to either x-axis or y-axis. So the desired line has an equation of the form y = (-1/7)x + b. Since the line y = 7x + 2 has slope 7, the desired line (that is, line AB) has slope -1/7 as well as passing through (2,9). So we first find the equation of the line through (2,9) that is perpendicular to the line y = 7x + 2. Then, using the fact that C is the midpoint of segment AB, we can finally determine point B.Įxample: suppose we want to reflect the point A(2,9) about the line k with equation y = 7x + 2. State the name of the mirror line and write its equation. Then we can algebraically find point C, which is the intersection of these two lines. Click hereto get an answer to your question The point ( - 2, 0) on reflection in a line is mapped to (2, 0) and the point (5, - 6) on reflection in the same line is mapped to ( - 5, - 6). So we can first find the equation of the line through point A that is perpendicular to line k. Graphing Stretches and Compressions of y logb(x) y log b ( x) When the parent function f (x) logb(x) f ( x) l o g b ( x) is multiplied by a constant a > 0, the result is a vertical stretch or compression of the original graph. Note that line AB must be perpendicular to line k, and C must be the midpoint of segment AB (from the definition of a reflection). Consider the graph of y ex (a) Find the equation of the graph that results from reflecting about the line y 4. Graph reflections of logarithmic functions. For example, horizontally reflecting the toolkit functions f\left(x\right)= were reflected over both axes, the result would be the original graph.Let A be the point to be reflected, let k be the line about which the point is reflected, let B represent the desired point (image), and let C represent the intersection of line k and line AB. Some functions exhibit symmetry so that reflections result in the original graph. There is no f(x) value give for x=-4 in the original function table, so the h(x) value is unknown.ĭetermine Whether a Functions is Even, Odd, or Neither When the graph of function yf(x) is reflected across the y-axis, the resultant graph is represented by the function yf(x). X=4 is unknown in the last problem because you are looking for what f(x) was when the x-value equaled -x, or in this case, -4.
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