Final answer:
The amplitude of y = -3cos(2x + 3) is 3, and the period is π. This cosine function is symmetric about the y-axis, and the first positive x-intercept can be found using a calculator's zero function.
Step-by-step explanation:
To determine the amplitude and period of the function y = –3cos(2x + 3), we need to examine the coefficients of the function and the argument of the cosine function.
The amplitude of the function is given by the absolute value of the coefficient in front of the cosine function, which in this case is |-3| = 3.
The period of a cosine function is 2π divided by the coefficient of x inside the cosine function, which in our case is 2. So, the period is 2π/2 = π.
This function graphs a cosine wave that has been reflected across the x-axis (due to the negative sign) and stretched vertically by a factor of 3. This function is symmetric about the y-axis since cosine functions are even functions.
To find the first positive x-intercept using a calculator, one would utilize the calculator's zero or root function. By graphing the function and then using the zero function, the calculator can determine the x-coordinate where the function first crosses the x-axis.