Mary Jane Sterling - Pre-Calculus - 1001 Practice Problems For Dummies (+ Free Online Practice)

An interesting feature of four of the trig functions is that they have asymptotes — those not-really-there lines used as guides to the shape of a curve. The sine and cosine functions don’t have asymptotes, because their domains are all real numbers. The other four functions have vertical asymptotes to mark where their domains have gaps.

In this chapter, you’ll work with the graphs of trigonometric functions in the following ways:

Marking any intercepts on the x -axis to help graph the curves

Locating and drawing in vertical asymptotes for the tangent, cotangent, secant, and cosecant functions

Computing the change in the period of a function based on some transformation

Adjusting the amplitude of the sine or cosine when the basic curve has a multiplier

Making sideways moves when transformations involve horizontal translations

Moving trig functions upward or downward with vertical translations

When graphing trigonometric functions, some challenges will include

Not misreading the period of the trig function when a transformation involves a fraction

Drawing enough full cycles of the curve to show its characteristics properly

Marking the axes appropriately for the situation

Making use of intercepts when they’re helpful in a graph

461–465Determine which trig function equation matches the graph.

461.

Illustration by Thomson Digital

(A)

(B)

(C)

(D)

(E)

462.

Illustration by Thomson Digital

(A)

(B)

(C)

(D)

(E)

463.

Illustration by Thomson Digital

(A)

(B)

(C)

(D)

(E)

464.

Illustration by Thomson Digital

(A)

(B)

(C)

(D)

(E)

465.

Illustration by Thomson Digital

(A)

(B)

(C)

(D)