Question
Consider the following functions ( $a$ ) $-(f) .$ Without graphing them, answer questions.a) $f(x)=2 \sin \left(\frac{1}{2} x-\frac{\pi}{2}\right)$b) $f(x)=\frac{1}{2} \cos \left(2 x-\frac{\pi}{4}\right)+2$c) $f(x)=-\sin \left[2\left(x-\frac{\pi}{2}\right)\right]+2$d) $f(x)=\sin (x+\pi)-\frac{1}{2}$e) $f(x)=-2 \cos (4 x-\pi)$ f) $f(x)=-\cos \left[2\left(x-\frac{\pi}{8}\right)\right]$Which functions have a graph with a phase shiftof $\frac{\pi}{4} ?$
Step 1
In a trigonometric function, the phase shift is the horizontal shift of the graph of the function. It is represented by the variable 'c' in the standard form of a trigonometric function, which is $f(x) = a \sin(bx + c) + d$ or $f(x) = a \cos(bx + c) + d$. Here, Show more…
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Consider the following functions ( $a$ )- ( $f$ ). Without graphing them, answer question. a) $f(x)=2 \sin \left(\frac{1}{2} x-\frac{\pi}{2}\right)$ b) $f(x)=\frac{1}{2} \cos \left(2 x-\frac{\pi}{4}\right)+2$ c) $f(x)=-\sin \left[2\left(x-\frac{\pi}{2}\right)\right]+2$ d $f(x)=\sin (x+\pi)-\frac{1}{2}$ e) $f(x)=-2 \cos (4 x-\pi)$ f) $(x)=-\cos \left[2\left(x-\frac{\pi}{8}\right)\right]$ Which functions have a graph with a phase shift of $\frac{\pi}{4} ?$
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Consider the following functions ( $a$ ) $-(f) .$ Without graphing them, answer questions. a) $f(x)=2 \sin \left(\frac{1}{2} x-\frac{\pi}{2}\right)$ b) $f(x)=\frac{1}{2} \cos \left(2 x-\frac{\pi}{4}\right)+2$ c) $f(x)=-\sin \left[2\left(x-\frac{\pi}{2}\right)\right]+2$ d) $f(x)=\sin (x+\pi)-\frac{1}{2}$ e) $f(x)=-2 \cos (4 x-\pi)$ f) $f(x)=-\cos \left[2\left(x-\frac{\pi}{8}\right)\right]$ Which functions have a graph with a period of $\pi ?$
Consider the following functions ( $a$ ) $-(f) .$ Without graphing them, answer questions. a) $f(x)=2 \sin \left(\frac{1}{2} x-\frac{\pi}{2}\right)$ b) $f(x)=\frac{1}{2} \cos \left(2 x-\frac{\pi}{4}\right)+2$ c) $f(x)=-\sin \left[2\left(x-\frac{\pi}{2}\right)\right]+2$ d) $f(x)=\sin (x+\pi)-\frac{1}{2}$ e) $f(x)=-2 \cos (4 x-\pi)$ f) $f(x)=-\cos \left[2\left(x-\frac{\pi}{8}\right)\right]$ Which functions have a graph with a period of $2 \pi ?$
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