Question

For each function, create a table that includes key values (such as max., min., and x-int.). Then go to your math tools and open the Graph tool to graph the function. Select the graph you created, copy it, and paste it in the space provided. Question 1 y = sec x

Answer 1

Secant function's graph oscillates, having vertical asymptotes at odd multiples of π/2 for x-intercepts.

The function y = sec(x) represents the secant function, which is the reciprocal of the cosine function. Let's create a table of key values and graph the function y = sec(x).

Table of Key Values:

To analyze the secant function, let's find its maxima, minima, and x-intercepts:

1. Maximum and Minimum:

The secant function has no maximum or minimum points as it oscillates indefinitely between -∞ and ∞.

2. X-intercepts:

The x-intercepts occur where the secant function has values of zero. Since the secant function is the reciprocal of the cosine function, its x-intercepts are where the cosine function equals zero.

The cosine function has x-intercepts at odd multiples of
`\((\pi)/(2)\)`. Hence, the x-intercepts for the secant function y = sec(x) occur at
`\(x = (\pi)/(2)`,
`-(\pi)/(2)`,
`(3\pi)/(2), -(3\pi)/(2), \dots\)`.

Graph of y = sec(x):

The graph shows the secant function \(y = \sec(x)\). As seen in the graph, the function has vertical asymptotes at its x-intercepts where the cosine function equals zero. The curve oscillates between these asymptotes, showcasing its periodic behavior.

The function is undefined at the x-intercepts, resulting in vertical asymptotes where the graph approaches positive or negative infinity. This graph visually demonstrates the periodic nature of the secant function and its behavior around the x-intercepts.