Final answer:
To sketch the graph of the function h(x)=2sec(π/4(x - 3)), we need to identify the stretching factor, period, and asymptotes. The stretching factor is 2, the period is 4, and the asymptotes are x = 3, x = 3 + π/4, x = 3 + 2π/4, and so on.
Step-by-step explanation:
To sketch the graph of the function h(x)=2sec(π/4(x - 3)), we need to identify the stretching factor, period, and asymptotes.
The stretching factor of the function is 2, which means the graph will be stretched vertically by a factor of 2 compared to the standard secant function.
The period of the function can be found by looking at the coefficient of x in the argument of the secant function. In this case, the coefficient is π/4, which means the period of the graph is π/(π/4) = 4.
The asymptotes of the graph can be found by looking at the values of x that make the secant function undefined. The secant function is undefined when the cosine function equals 0, which occurs at x = 3 + nπ/4, where n is an integer. So, the asymptotes of the graph are x = 3, x = 3 + π/4, x = 3 + 2π/4, and so on.