How do you find the critical points to graph #f(x) = 4 sin(x -pi/2 )#?

1 Answer
Dec 12, 2015

Answer:

#(pi/2,0)#, #(pi,4)#, #((3pi)/2,0)#, #(2pi,-4)#, #((5pi)/2,0)#

Explanation:

By the five-point method, you need five points to graph the function, #f(x)=4sin(x-pi/2)#. To find the five points, first find the five points for its parent function #e(x)=sinx#. Ignore the negative x values and its corresponding y values in the table below.

http://bscstudent.buffalostate.edu/kajfkr79/web/Masters_Project/Graphing_the_Sine_Curve.html

Now that you have the five points for the parent function, use the mapping rule to apply transformations in order to find the five points for the transformed function, #f(x)=4sin(x-pi/2)#.

Mapping rule: #(x+color(red)(pi/2),color(blue)4y)#

#f(x)=4sin(x-pi/2)#
Point #1. (0+color(red)(pi/2), color(white)(xxx)(color(blue)4)0) rArr color(white)(xxxxxxxxx)(pi/2,0)#
Point #2. (pi/2+color(red)(pi/2), color(white)(xx)(color(blue)4)1) rArr color(white)(xxxxxxxxx)(pi,4)#
Point #3. (pi+color(red)(pi/2), color(white)(xxx)(color(blue)4)0) rArr color(white)(axxxxxxxx)((3pi)/2,0)#
Point #4. ((3pi)/2+color(red)(pi/2), color(white)(ix)(color(blue)4)(-1)) rArr color(white)(xxxxxx)(2pi,-4)#
Point #5. (2pi+color(red)(pi/2), color(white)(xx)(color(blue)4)0) rArr color(white)(xxxxxxxxx)((5pi)/2,0)#

The transformed graph would look like:

https://www.desmos.com/screenshot/6bf4rdat0g

Zoom in to check the five main points shown on the graph.