Practices for Math 140

  1. Define a function $f$, whose graph is similar to the cosine function, $\cos x,$ and satisfies ALL the following conditions:

    1. the period of $f$ is $4\pi ,$

    2. the function $f$ has amplitude of $4,$

    3. the function $f$ has a maximum value of $2$ when $x=2\pi .$[hint: You need to come up with ONE function that satisfies All the conditions (a), (b), and (c); think of changing the period, amplitude, reflection, and shifting of $y=\cos x.]$

    [hint: y=-4cos((1/2)*x)-2].

  2. Explain why MATH graphically.  [because if you shift y=sin(x) to the left pi/2 units, you will get y=cos(x)]

  3. Express $\sin (x)$ in terms of $\cos x.$

  4. If MATH

    1. Find the period of $f.$ [**the period is 2*pi divides by (1/3) so it is 6*pi].

    2. Find the asymptotes for $f.$ [**a typo here, it is supposed to be amplitude, the amplitude is 2].

    3. Sketch $\ y=f(x)$

    4. Explain the relationship between the graphs of $y=\cos x$ and MATH [hint: MATHis being reflected along x-axis from $y=\cos x$ and change the amplitude from 1 to 2 and the period of MATHis 6*pi.

  5. Find the function whose graph is the reflection of $y=\cos x$ along the $y-axis.$ [hint: y=cos(-x)]

  6. Find the function whose graph is the reflection of $y=\sin (-x)$ along the $x-axis.$ [hint: y=-sin(-x)].

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