91Ó°ÊÓ

The function we're given, \(g(x) = \sin(-5x)\), is a sine function with the general form \(f(x) = A\sin(Bx + C)\). We know that A = 1, B = -5, and C = 0.

The amplitude is the absolute value of A. In our case, A = 1, so the amplitude is simply \(|1| = 1\).

The period of a sine function is given by the formula \(P = \frac{2Ï€}{|B|}\). In our case, B = -5, so the period is \(P = \frac{2Ï€}{|-5|} = \frac{2Ï€}{5}\).

The range of a sine function with amplitude A is the interval \([-A, A]\). In our case, the amplitude is 1, so the range of the function is \([-1, 1]\).

To sketch the graph, we take the following steps: 1. Identify the x-axis as the horizontal division between our minimum and maximum range. 2. Mark equal intervals for the period along the x-axis. 3. Place the sine curve, taking into account the amplitude, period, and range. 4. Ensure that the graph covers the interval \([-π, π]\). Take observations from Steps 2 to 4, ensuring the amplitude is 1, the period is \(\frac{2π}{5}\), and the range is \([-1, 1]\). Now we have successfully completed all the tasks. a) The graph of the function g(x) is sketched on the interval \([-π, π]\) with amplitude = 1, period = \(\frac{2π}{5}\), and range between -1 and 1. b) The range of g(x) is \([-1, 1]\). c) The amplitude of g(x) is 1. d) The period of g(x) is \(\frac{2π}{5}\).