Tangent Graphs

Front

What is the period of the function y = tan(kx)?

Back

Front

What is the vertical shift of the graph y = tan(x) + c?

Back

The vertical shift of the graph is determined by the value of c. If c > 0, the graph shifts up; if c < 0, it shifts down.

Front

What is the general form of the tangent function?

Back

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

Front

How do you find the vertical asymptotes of the tangent function?

Back

Front

What is the phase shift of the function y = tan(x - c)?

Back

The phase shift is c units to the right if c > 0 and c units to the left if c < 0.

Front

What is the effect of changing the coefficient of x in y = tan(kx)?

Back

Front

What is the range of the tangent function?

Back

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

Front

What happens to the graph of y = tan(x) when k is negative?

Back

If k is negative, the graph of y = tan(kx) is reflected across the y-axis.

Front

What is the relationship between the tangent function and the sine and cosine functions?

Back

Front

How do you determine the vertical shift of the function y = tan(x) + d?

Back

The vertical shift is determined by the value of d. If d > 0, the graph shifts up; if d < 0, it shifts down.