Question

Can someone please show me in steps and an easy explanation on how to do these problems?? I'm having a hard time trying to understand this and my teacher's explanation was too confusing. I will give brainliest to the best answer!


Graph: f(x)=sin(x)-2

Graph: f(x)=cos(2x)+1

Answer 1

Answer:

f(x) = sin(x) - 2, ⇒     the graph will be complete cycle from 0° to 360° on the x-axis and between -3 and -1 on the y-axis

f(x) = cos(2x) + 1, ⇒ the graph will be 2 complete cycle from 0° to 360° on the x-axis and between 0 and 2 on the y-axis

Step-by-step explanation:

To graph f(x) = sin(x) - 2⇒ use this values of x (the period of x is 90)

The values of x = 0° , 90° , 180° , 270° , 360° (the domain 0°≤x≤360° complete cycle)

Then find the corresponding values of f(x)

f(0) = sin(0) - 2 = 0 - 2 = -2 ⇒ (0 , -2)

f(90) = sin(90) - 2 = 1 - 2 = -1 ⇒ (90 , -1)

f(180) = sin(180) - 2 = 0 - 2 = -2 ⇒(180 , -2)

f(270) = sin(270) - 2 = -1 - 2 = -3 ⇒ (270 , -3)

f(360) = sin(360) - 2 = 0 - 2 = -2 ⇒ (360 , -2)

Graph these points ( the graph will be complete cycle from 0° to 360° on the x-axis and between -3 and -1 on the y-axis)

To graph f(x) = cos(2x) + 1 ⇒ use this values of x ( the period of x is 90°/2=45 °because the angle in f(x) is 2x)

The values of x is 0° , 45° , 90° , 135° , 180° , 225° , 270° , 315° , 360°

(The domain 0°≤x≤360°, for 2x is 0°≤2x≤720° complete cycle)

Then find the corresponding values of f(x)

f(0) = cos(2×0) + 1 = 1 + 1 = 2 ⇒ (0 , 2)

f(45) = cos(2×45) + 1 = 0 + 1 = 1 ⇒ (45 , 1)

f(90) = cos(2×90) + 1 = -1 + 1 = 0 ⇒ (90 , 0)

f(135) = cos(2×135) + 1 = 0 + 1 = 1 ⇒ (135 , 1)

f(180) = cos(2×180) + 1 = 1 + 1 = 2 ⇒ (180 , 2)

f(225) = cos(2×225) + 1 = 0 + 1 = 1 ⇒ (225 , 1)

f(270) = cox(2×270) + 1 = -1 + 1 = 0 ⇒ (270 , 0)

f(315) = cos(2×315) + 1 = 0 + 1 = 1 ⇒ (315 , 1)

f(360) = cos(2×360) + 1 = 1 + 1 = 2 ⇒ (360 , 2)

Graph these points ( the graph will be 2 complete cycle from 0° to 360° on the x-axis and between 0 and 2 on the y-axis)

Answer 2

1. Answer:  see graph

Step-by-step explanation:

The standard equation for sin is: y = A sin (Bx - C) + D     where

• A is the amplitude
• $\dfrac{2\pi}{B}$ is the period
• $\dfrac{C}{B}$ is the phase shift (horizontal shift)
• D is the vertical shift

A and D affect the y-value using the order of operations.

B and C affect the x-value using the opposite order of operations.

You NEED to know how to graph the parent function of y = sin (x) in order to graph the transformed (new) function.

First, create a table for y = sin (x)   refer to the Unit Circle   then find the  coordinates of the new equation y = sin(x) - 2.  Notice that the only thing that changes is that  D = -2 (which means the graph is shifted down 2 units).

$\qquad y=sin(x)\qquad y=sin(x)-2\\\begin {array}{c|c||c|c}\underline{\qquad x\qquad &\underline{\ y\ }}&\underline{x}&\underline{y-2}\\ 0^o=0&0&0&-2\\\\90^o=\dfrac{\pi}{2}&1&\dfrac{\pi}{2}&-1\\\\180^o=\pi&0&\pi &-2\\\\270^o=\dfrac{3\pi}{2}&-1&\dfrac{3\pi}{2}&-3\\\\360^o=2\pi&0&2\pi &-2\\\\\end{array}$

Now plot the points for the new graph (see attached graph)

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2. Answer:  see graph

Step-by-step explanation:

The standard equation for cos is: y = A cos (Bx - C) + D

(see #1 above for info)

$\qquad y=cos(x)\qquad y=cos(2x)+1\\\begin {array}{c|c||c|c}\underline{\qquad x\qquad &\underline{\ y\ }}&\underline{x\div 2}&\underline{y+1}\\ 0^o=0&1&0&2\\\\90^o=\dfrac{\pi}{2}&0&\dfrac{\pi}{4}&1\\\\180^o=\pi&-1&\dfrac{\pi}{2} &0\\\\270^o=\dfrac{3\pi}{2}&0&\dfrac{3\pi}{4}&1\\\\360^o=2\pi&1&\pi &2\\\\\end{array}$

Now plot the points for the new graph (see attached graph)