Trigonometry Workbook For Dummies
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Adding a number to a tangent function results in raising the curve on the graph by that amount. Likewise, subtracting a number drops the curve.

The tangent function raised and lowered by 3 units.
The tangent function raised and lowered by 3 units.

Because the tangent function has values from negative infinity to positive infinity, adding to or subtracting from the function doesn’t change what values the tangent has — it just changes where they happen. When you add or subtract, the point of inflection in the tangent curve (where the curve appears to flatten out a bit) shifts up or down. The preceding figure shows some graphs to illustrate this shift.

Adding or subtracting a number from the angle variable of the tangent function has the same effect as with the sine and cosine — it moves the curve to the left or right. The graph of y = tan (x + 1) shifts one unit to the left, including the asymptotes. The graph of y = tan (x – 1) moves everything to the right one unit. The following figure shows a comparison of the tangent function and the two shifted curves.

The tangent function moved left and right 1 unit.
The tangent function moved left and right 1 unit.

If you have a tough time telling these graphs apart, just look for the point of inflection of the tangent curve. The point of inflection is a good reference mark when looking at all these variations.

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Mary Jane Sterling taught algebra, business calculus, geometry, and finite mathematics at Bradley University in Peoria, Illinois, for more than 30 years. She is the author of several For Dummies books, including Algebra Workbook For Dummies, Algebra II For Dummies, and Algebra II Workbook For Dummies.

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