graph the following function: $y = 3-\frac{5}{2}cot(x)$\nstep 2 of 2: determine how the general shape of the…
graph the following function: $y = 3-\frac{5}{2}cot(x)$\nstep 2 of 2: determine how the general shape of the graph, chosen in the previous step, would be shifted, stretched, and reflected for the given function. graph the results on the axes provided.\nanswer\nx - axis reflection\nreflect graph across x - axis\nshift graph vertically\nup down none\nshift graph horizontally (phase shift)\nleft right none\nstretch/compress graph vertically\nyes no\nstretch/compress graph horizontally (period)\nyes no
Answer
Explanation:
Step1: Analyze the general form of cotangent function transformation
The general form of a cotangent - like function is (y = A\cot(Bx - C)+D). For the function (y = 3-\frac{5}{2}\cot(x)), we can rewrite it as (y=-\frac{5}{2}\cot(x)+3). Here (A =-\frac{5}{2}), (B = 1), (C = 0), and (D = 3).
Step2: Check for (x) - axis reflection
The coefficient of (\cot(x)) is (-\frac{5}{2}). Since the coefficient of (\cot(x)) is negative, there is an (x) - axis reflection.
Step3: Check for vertical shift
The value of (D = 3). A positive value of (D) means the graph is shifted up.
Step4: Check for horizontal shift (phase - shift)
Since (C = 0) in (y = A\cot(Bx - C)+D), there is no horizontal shift.
Step5: Check for vertical stretch/compression
The absolute value of (A=\left|-\frac{5}{2}\right|=\frac{5}{2}>1), so there is a vertical stretch.
Step6: Check for horizontal stretch/compression (period)
The period of the basic cotangent function (y = \cot(x)) is (\pi), and for (y = A\cot(Bx - C)+D), the period is (T=\frac{\pi}{|B|}). Since (B = 1), the period remains (\pi), so there is no horizontal stretch/compression.
Answer:
x - Axis Reflection: Reflect graph across x - axis Shift Graph Vertically: Up Shift Graph Horizontally (Phase Shift): None Stretch/Compress Graph Vertically: Yes Stretch/Compress Graph Horizontally (Period): No