How do you shift and graph $y = - 3 + sin x$ $y=-3+sinx$ ?

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Answer 1 · 2014-10-31T23:20:19

The period of $sin$ $sin$ is $2 π$ $2pi$ .

The $- 3$ $-3$ is applied to the result of $sin (x)$ $sin(x)$ which affects the $y$ $y$ value.

All of the points will be shifted down $3$ $3$ units.

Rely on your knowledge of the unit circle to figure out the values of sin on the $x$ $x$ and $y$ $y$ axis.

$f (0) = - 3 + sin (0) = - 3 + 0 = - 3 \to (0, - 3)$ $f(0)=-3+sin(0)=-3+0=-3 -> (0,-3)$

$f (\frac{π}{2}) = - 3 + sin (\frac{π}{2}) = - 3 + 1 = - 2 \to (\frac{π}{2}, - 2)$ $f(pi/2)=-3+sin(pi/2)=-3+1=-2 -> (pi/2,-2)$

$f (π) = - 3 + sin (π) = - 3 + 0 = - 3 \to (π, - 3)$ $f(pi)=-3+sin(pi)=-3+0=-3 -> (pi,-3)$

$f (\frac{3 π}{2}) = - 3 + sin (\frac{3 π}{2}) = - 3 - 1 = - 4 \to (\frac{3 π}{2}, - 4)$ $f((3pi)/2)=-3+sin((3pi)/2)=-3-1=-4 -> ((3pi)/2,-4)$

$f (2 π) = - 3 + sin (2 π) = - 3 + 0 = - 3 \to (2 π, - 3)$ $f(2pi)=-3+sin(2pi)=-3+0=-3->(2pi,-3)$

Enter the function into the calculator

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Set the interval, XMIN and MAX , from $[0, 2 π] \to 2 π = 6.283185307$ $[0,2pi] -> 2pi=6.283185307$

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Press the GRAPH button

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How do you shift and graph y=−3+sinxy=-3+sinx?