Advertisement
Online Test Banks
Score higher
See Online Test Banks
eLearning
Learning anything is easy
Browse Online Courses
Mobile Apps
Learning on the go
Explore Mobile Apps
Dummies Store
Shop for books and more
Start Shopping

Translating Tangent Functions on a Graph

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.

  • Add a Comment
  • Print
  • Share
blog comments powered by Disqus
Advertisement
Advertisement

Inside Dummies.com

Dummies.com Sweepstakes

Win an iPad Mini. Enter to win now!