Analyze the function f(x) = - tan 4x. include:
- domain and range
- period
- two vertical asymptotes

- Domain: Domain is the group of x values that makes the function defined. The tangent curve is undefined at

4x=pi/2. This translates to a domain of x=/=pi/8, 3pi/8, 5pi/8, 7pi/8, etc,.

- Range: The range would be from negative infinity to positive infinity.

- Period: Since, the frequency of this function is 4, the period would be pi/4 because one complete tangent curve would be completed every pi/4 radians.

- Two vertical asymptotes: There would be a vertical asymptote at x=pi/8 & x=3pi/8. Since, the function would be undefined at those points.

answer: 20

step-by-step explanation: subtract the minimum date value from the maximum data value to find the date range. in this casem the date range is 42 - 22 = 20

hope this ! : ) ~zane