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Mathematics 18 Online
OpenStudy (anonymous):

Write the equation of the tangent function with standard period, phase shift of pi/2, and a vertical shift of 2. a. f(x)=tan(x-2)+pi/2 b. f(x)=2tan(x-pi/2) c. f(x)=2tan(x+pi/2)+2 d. f(x)-tan(x-pi/2)+2 Please walk me through it.

OpenStudy (ybarrap):

If you have a function, say y=x/3, you know that it has to go through <0,0> because at x=0, y=0. If I want to shift this "upwards" by 2 then I just need to add 2 to y: y = x/3 + 2. This means now that at x=0, y=2, where before we had at x=0, y=0. Ok, this takes of the shift upwards. Let's look at phase shift. Phase shift means move the function, y left or right. If I want to shift y=x/3 to the right, I would replace x with x - 3. If I want to move y to the the left, I would replace x with x + 3. For example, lets shift y=x/3 right by pi/2. We replace x with x - pi/2 to get y=(x-pi/2)/3. This means that at x=pi/2 that y=0: <pi/2,0>. Recall that y=0 before only when x=0, but now that we added a shift, we are at y=0 only when we delay or "phase shift" the function by pi/2. This takes care of shifts up/down and left right. Does this make sense?

OpenStudy (anonymous):

I think so. Thanks.

OpenStudy (ybarrap):

Which of your answers represents an upward shift by 2 and a sideways shift by pi/2?

OpenStudy (ybarrap):

sideways shift by pi/2: replace x with x - pi/2 or x+pi/2, depending on which way we want to shift up/down shift by 2: replace f(x) with f(x) \(\pm\) 2, depending on whether we want to shift up or down take f(x) = 2tan(x) Shift left by pi/2: f(x) = 2tan(x+pi/2) Shift up by 2: f(x) = 2tan(x) + 2 Combine results to get: f(x)=2tan(x+pi/2) + 2

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