![]() In such a graph, nothing has been reflected across the x-axis. The answer is yes, if you're talking about a parabola that opens upward and the bottom part of that parabola lies below the x-axis. Please feel free to add any questions you may have. I hope these images help you understand what reflections are. This effectively reflects every point (except for the x-intercepts) across the x-axis, flipping the entire parabola. Every y-value that was positive in the first graph above becomes negative, and every y-value that was negative becomes positive. If we multiply the polynomial by -1, then the entire parabola is reflected across the x-axis. ![]() If we plot the absolute value of 2x^2-16x-16, instead, then the part below the x-axis above will be reflected across that axis, in the new graph. Part of the parabola lies below the x-axis, two points of the parabola lie directly on the x-axis, and the remaining part of the parabola lies entirely above the x-axis. In such a graph, nothing has been reflected. All rights reserved.Click to expand.Hi Erin. Now try some problems that test your knowledge of graphical transformationsīiology Project > Biomath > Transformations > ReflectionsĪll contents copyright © 2006. As you can see, the graph of y 2( x) is in fact the base graph g( x) reflected across the y-axis. Y 2( x) = g( -x) = (- x) 3 - (- x) 2 -4(- x) + 4 = - x 3 + x 2 + 4 x + 4,Ĭonstruct a table of values, and plot the graph of the new function. Look like? Using our knowledge of reflections across the y-axis, the graph of y 2( x) should look like the base graph g( x) reflected across the y-axis. Take a look at the graphs of f ( x) and y 1( x).įunction (2), g( x), is a cubic function. īased on the definition of reflection across the y-axis, the graph of y 1( x) should look like the graph of f ( x), reflected across the y-axis. The graphical representation of function (1), f ( x), is a parabola shifted 1 unit to the right. Of course, y-intercepts will remain unchanged under this type of reflection.Įxamples of Reflections Across the y-Axis In other words, all of the portions of the graph to the left of the y-axis will be reflected to the corresponding position to the right of the y-axis, while all of the portions of the graph to the right of y-axis will be reflected to the corresponding positions to the left of the y-axis. Symbolically, we define reflections across the y-axis as follows:Ĭan be sketched by reflecting f ( x) across the y-axis. You can visualize a reflection across the y-axis by imagining the graph that would result from folding the base graph along the y-axis. As you can see, the graph of y 2( x) is in fact the base graph g( x) reflected across the x-axis. Y 2( x) = -g( x) = -(| x| + 1) = - | x| -1 ,Ĭonstruct a table of values, and plot the graph of the new function. Look like? Using our knowledge of reflections across the x-axis, the graph of y 2( x) should look like the base graph g( x) reflected across the x-axis. Take a look at the graphs of f ( x) and y 1( x).įunction (2), g( x), is an absolute value function. Y 1( x) = -f ( x) = -( x 2-9) = - x 2 + 9.īased on the definition of reflection across the x-axis, the graph of y 1( x) should look like the graph of f ( x), reflected across the x-axis. Looks like? Using the definition of f ( x), we can write y 1( x) as, The graphical representation of function (1), f ( x), is a parabola shifted 9 units down with respect to the base function y = x 2. ![]() Of course, x-intercepts will remain unchanged under this type of reflectionĮxamples of Reflections Across the x-Axis In other words, all of the portions of the graph above the x-axis will be reflected to the corresponding position below the x-axis, while all of the portions of the graph below the x-axis will be reflected above the x-axis. Symbolically, we define reflections across the x-axis as follows:įor the base function f ( x), the function given byĬan be sketched by reflecting f ( x) across the x-axis. To visualize a reflection across the x-axis, imagine the graph that would result from folding the base graph along the x-axis. We will discuss two types of reflections: reflections across the x-axis and reflections across the y-axis. Biology Project > Biomath > Transformations > Reflections Transformations of Graphs
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