document.write( "Question 152652: Which of the following is a reflection of f(x) = -x + 1 about the x-axis?
\n" ); document.write( " r(x) = x + 1
\n" ); document.write( " r(x) = x - 1
\n" ); document.write( " r(x) = -( x - 1)
\n" ); document.write( " None of the above
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Algebra.Com's Answer #112288 by mducky2(62) $\"\"$ $\"About$

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Let's sketch f(x) = -x + 1. All linear equations can be represented as f(x) = mx + b. The m is the slope of the line. We know it has the same slope. Therefore, the graph above will have the same slope as f(x) = -x + 1.
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The b is the y-intercept at the point (0,b). In this case, b = 1. So we know it intersects the y-axis at the point (0,1):
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$\"+graph%28+200%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+-x%2B1%29+\"$
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Now let's try to figure out what the reflection looks like. In order to be a reflection of f(x) = -x + 1, it should have the opposite slope and opposite y-intercept.
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Since the slope of the original function is m = -1, the opposite slope would be m = 1.
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Since the intercept is one unit above the x-axis, the next time, it should be one unit below. That would be at the point (0,-1) or b = -1.
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Putting that all together:
\n" ); document.write( "r(x) = mx + b
\n" ); document.write( "r(x) = (1)x + (-1)
\n" ); document.write( "r(x) = x - 1
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Graphing that equation:
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$\"+graph%28+200%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+x-1%29+\"$
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Now let's graph both equations to make sure they are reflections of each other:
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$\"+graph%28+200%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+-x%2B1%2C+x-1%29+\"$
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They are reflections of each other. Therefore, the answer is r(x) = x - 1. \n" ); document.write( "

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