What is the period of the tangent function $$f(x) = \tan(Bx)$$ ?

The period of the tangent function is given by $$\frac{\pi}{|B|}$$ .

How do you determine the phase shift of the tangent function $$f(x) = \tan(Bx + C)$$ ?

The phase shift is determined by the formula $$-\frac{C}{B}$$ .

What is the equation of the tangent function with a vertical shift of 1 unit up?

The equation is $$f(x) = \tan(x) + 1$$ .

How do you find the x-intercepts of the tangent function?

The x-intercepts of the tangent function occur where $$f(x) = 0$$ , which is at $$x = n\pi$$ , where n is any integer.

What is the relationship between the cotangent and tangent functions?

The cotangent function is the reciprocal of the tangent function: $$\cot(x) = \frac{1}{\tan(x)}$$ .

What is the effect of a negative A in the tangent function?

A negative A reflects the graph across the x-axis.

What is the equation of the tangent function that has a period of $$\pi$$ ?

The equation is $$f(x) = \tan(2x)$$ , since the period is given by $$\frac{\pi}{|B|}$$ and B = 2.

Where are the vertical asymptotes of the function $$f(x) = \tan(\frac{x}{4})$$ ?

The vertical asymptotes are at $$x = -2\pi, 0, 2\pi$$ .

What is the transformation represented by the function $$f(x) = \tan(x + \frac{\pi}{4})$$ ?

This function represents a phase shift of $$-\frac{\pi}{4}$$ to the left.

Tangent Graphs Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the general form of a tangent function?

Back

2.

FLASHCARD QUESTION

Front

Back

3.

FLASHCARD QUESTION

Front

How does the value of A in the tangent function affect the graph?

Back

The value of A in the tangent function affects the vertical stretch or compression of the graph. If A > 1, the graph is stretched; if 0 < A < 1, it is compressed.

4.

FLASHCARD QUESTION

Front

Back

The vertical shift is down 2 units.

5.

FLASHCARD QUESTION

Front

What are the asymptotes of the tangent function?

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

Back

Changing B affects the period of the function. A larger value of B results in a shorter period.

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