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: 1) twenty-seven times y

              2) twenty-seven multiplied by y

spinning a 1, 2, or 3. option d.

step-by-step explanation: when spinning a number graph up to 4, and aiming for any number less than 3, that automatically eliminates the number 4. now you have two numbers to spin on that are less than 3, but the number 3 is included in this question because it's no greater of an number than itself. i hope this you : )