Question
Let f(x) = cos x.
Complete parts (a) through (e) below
a. What is the y-intercept of the graph of f?
b. For what numbers x, -π ≤ x ≤ π, is the graph of f increasing?
c. What is the absolute minimum value of f?
d. For what numbers x, 0 ≤ x ≤ 2π, does f(x) = 0?
e. What are the x-intercepts of f?
Complete parts (a) through (e) below
a. What is the y-intercept of the graph of f?
b. For what numbers x, -π ≤ x ≤ π, is the graph of f increasing?
c. What is the absolute minimum value of f?
d. For what numbers x, 0 ≤ x ≤ 2π, does f(x) = 0?
e. What are the x-intercepts of f?
Answers
GPT 3.5
a. The y-intercept of the graph of f(x) = cos(x) is (0, 1).
b. The graph of cos(x) is increasing for x values between -π/2 and π/2. Therefore, the numbers -π/2 ≤ x ≤ π/2 are the values for which the graph of f is increasing.
c. The absolute minimum value of cos(x) is -1.
d. The function cos(x) = 0 at x = π/2 and x = 3π/2 (as well as any integer multiple of π).
e. The x-intercepts of cos(x) are at x = π/2 + nπ and x = 3π/2 + nπ, where n is an integer. These x-intercepts correspond to the points where the graph of cos(x) crosses the x-axis.
b. The graph of cos(x) is increasing for x values between -π/2 and π/2. Therefore, the numbers -π/2 ≤ x ≤ π/2 are the values for which the graph of f is increasing.
c. The absolute minimum value of cos(x) is -1.
d. The function cos(x) = 0 at x = π/2 and x = 3π/2 (as well as any integer multiple of π).
e. The x-intercepts of cos(x) are at x = π/2 + nπ and x = 3π/2 + nπ, where n is an integer. These x-intercepts correspond to the points where the graph of cos(x) crosses the x-axis.