Math question help

Question

Graph the following function: y=−1+52cot(x)

Step 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.

x- Axis Reflection:

Shift Graph Vertically:

Shift Graph Horizontally (Phase Shift):

Stretch/Compress Graph Vertically:

Stretch/Compress Graph Horizontally (Period):

Answer 1

Remember the standard form of trig functions, specifically cotx. You should be able to find this in your class notes or in the textbook.

The standard form of the cotangent function is:

y = A cot (Bx-C) + D

From the variables in this equation, we can identify some important facts about the graph of a specific cotangent function.

The value of A, which is also known as the amplitude of the function tells you whether the graph is reflected over the x-axis. If A is a positive number, then there is no reflection. If A is a negative number, then the graph is reflected over the x-axis.

The value of D tells you the Vertical Shift of the function. If D is a positive number, the graph shifts upwards. If D is a negative number, the graph shifts downwards. If D is 0, there is no vertical shift.

The Horizontal Shift (Phase Shift) of the function is determined by the value of C. If C is negative, then the graph has a left shift. If C is positive, then the graph has a right shift. If C is zero, there is no horizontal shift.

The value of A tells you the Vertical Stretch/Compression of the function. If it is number greater than 1, then the function is vertically stretched. If it is a fraction or decimal less than 1, then the graph is vertically compressed. If A equals 1, there is no vertical stretch/compression.

The value of B can help you calculate the period of the function. You just plug the value of B into the equation period = 2pi/B and that gives you the value of the period of the function. If B is a number greater than 1, the graph is horizontally compressed. If B is a fraction or decimal less than 1, the graph is horizontally stretched. If B is 1, there is no horizontal compression/stretch.

Now you just need to identify the variables in the given equation

1. Rearrange the equation in standard form

You should have y = 52cotx - 1

Now identify the values of A, B, C, and D

A is 52

B is 1

C is 0

D is -1

From this information, you can now identify the values the question asks you to find.