# How do you graph f(x)= 1+ cosx ?

Apr 23, 2018

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#### Explanation:

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To graph color(red)(f(x)=1+Cos(x),

start working on it's Parent Function color(blue)(f(x) = Cos(x) first.

Make a table of values for $f \left(x\right) = C o s \left(x\right) \mathmr{and} f \left(x\right) = 1 + \cos \left(x\right)$

For color(red)(x, consider the values color(red)(0, pi/2, pi, (3pi)/2 and 2pi.

If you examine color(green)("Col 4" and "Col 5", you see that the difference is 1.

color(red)("Graph of y = f(x) = Cos(x)"

color(red)("Graph of y = f(x) = 1 + Cos(x)"

$\textcolor{red}{\text{Graph of y = f(x) = Cos(x)}}$ & color(blue)("y = f(x) = 1 + Cos(x)"

Use color(green)(y=A*sin(Bx+C)+D [ or ]

use color(green)(y=A*cos(Bx+C)+D,

where, Amplitude is $| A |$

Period is $\frac{2 \pi}{B}$ and

Vertical Shift is $D$

Since $D = 1$, the graph is shifted vertically by 1 unit.

If $D$ is given, the value of $D$ is responsible for a vertical shift.

Hope it helps.