But this needn’t be!
Four simple rules govern all transformation questions encountered on the SAT/ACT. Master these laws, and all such questions suddenly become easy ones.
Listed below is what you need to know.
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Horizontal Reflection (across the y-axis)
Listed below is what you need to know.
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Horizontal Reflection (across the y-axis)
Replace x with -x.
For example: If f(x) = x^2– x+1, the horizontal reflection is f(x) = (-x)^2–(-x)+1 = x^2+x+1.
Vertical Reflection (across the x-axis)
Vertical Reflection (across the x-axis)
Replace y with -y.
For example: If g(x) = 3x–2 i.e. y = 3x–2, the vertical reflection is (-y) = 3x–2 and y = -3x+2. Therefore, g(x) = -3x+2.
Horizontal Shift, h units
For example: If g(x) = 3x–2 i.e. y = 3x–2, the vertical reflection is (-y) = 3x–2 and y = -3x+2. Therefore, g(x) = -3x+2.
Horizontal Shift, h units
Replace x with x–h.
For example: If f(x) = x^2–x is shifted 4 units left, h = -4, h–k = h–(-4) = h+4, and the shifted function is f(x) = (x+4)^2–(x+4) = x^2+8x+16–x–4 = x^2+7x+12.
Vertical Shift, k units
For example: If f(x) = x^2–x is shifted 4 units left, h = -4, h–k = h–(-4) = h+4, and the shifted function is f(x) = (x+4)^2–(x+4) = x^2+8x+16–x–4 = x^2+7x+12.
Vertical Shift, k units
Replace y with y-k (or simply add k to the function).
For example: If y = |6x–1| is shifted 3 units up, k = 3, y–k = y–3, and the shifted function is y–3 = |6x–1|. Therefore, y |6x–1|+3.
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For practice, search Google for worksheets covering any or all topics listed above, pick a worksheet that provides answers, complete the worksheet, analyze any mistakes, and redo it until you can complete that worksheet with no errors. Then repeat, with additional worksheets, as needed, until you’ve mastered this material.
For example: If y = |6x–1| is shifted 3 units up, k = 3, y–k = y–3, and the shifted function is y–3 = |6x–1|. Therefore, y |6x–1|+3.
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For practice, search Google for worksheets covering any or all topics listed above, pick a worksheet that provides answers, complete the worksheet, analyze any mistakes, and redo it until you can complete that worksheet with no errors. Then repeat, with additional worksheets, as needed, until you’ve mastered this material.
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