select the correct answer. which statement is true about the tangent function? a. the tangent function has…

select the correct answer. which statement is true about the tangent function? a. the tangent function has an amplitude and midline but no period. b. the tangent function has a midline but no period and no amplitude. c. the tangent function has a period but no amplitude and no midline. d. the tangent function has a midline and period but no amplitude.

select the correct answer. which statement is true about the tangent function? a. the tangent function has an amplitude and midline but no period. b. the tangent function has a midline but no period and no amplitude. c. the tangent function has a period but no amplitude and no midline. d. the tangent function has a midline and period but no amplitude.

Answer

Explanation:

Step1: Recall tangent - function properties

The general form of the tangent function is (y = A\tan(Bx - C)+D).

Step2: Analyze period

The period of the tangent function (y = A\tan(Bx - C)+D) is (T=\frac{\pi}{|B|}), so it has a period.

Step3: Analyze amplitude

The tangent function does not have a well - defined amplitude because its range is ((-\infty,\infty)), so it has no amplitude.

Step4: Analyze mid - line

The mid - line of the tangent function (y = A\tan(Bx - C)+D) is (y = D), so it has a mid - line.

Answer:

D. The tangent function has a midline and period but no amplitude.