Tangent Graph

Front

What is the definition of the tangent function?

Back

The tangent function, denoted as tan(x), is defined as the ratio of the opposite side to the adjacent side in a right triangle. It can also be expressed as tan(x) = sin(x)/cos(x).

Front

What is the period of the tangent function?

Back

Front

What is the vertical asymptote of the tangent function?

Back

Front

How do you find the phase shift of a tangent function?

Back

The phase shift of a tangent function of the form y = tan(k(x - d)) is given by d. It represents a horizontal shift of the graph.

Front

What is the vertical shift in the function y = tan(x) + 1?

Back

The vertical shift is 1, meaning the entire graph of the tangent function is shifted up by 1 unit.

Front

What is the range of the tangent function?

Back

The range of the tangent function is all real numbers, (-∞, ∞).

Front

How does the coefficient of x affect the tangent function's graph?

Back

The coefficient of x in the tangent function affects its period. A larger coefficient results in a shorter period.

Front

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

Back

A negative coefficient in the tangent function reflects the graph across the x-axis.

Front

What is the general form of the tangent function?

Back

The general form of the tangent function is y = a * tan(k(x - d)) + c, where a is the vertical stretch, k is the horizontal stretch, d is the phase shift, and c is the vertical shift.

Front

What is the phase shift of the function y = tan(2(x - rac{ ext{π}}{4}))?

Back