1. Identify the max and min y-values. 2. Use the formula: $amplitude = \frac{|max - min|}{2}$.

1. Identify one complete cycle. 2. Measure the horizontal distance of that cycle.

1. Identify the max and min y-values. 2. Calculate the midline: $midline = \frac{max + min}{2}$. 3. The midline value is the vertical shift 'd'.

1. Choose a key point (e.g., starting point of a sine or cosine wave). 2. Compare its position to the standard sine or cosine graph. 3. Determine the horizontal distance it has shifted.

1. Find the period. 2. Use the formula $b = \frac{2\pi}{period}$.

1. Find a, b, c, and d. 2. Use the general form: $f(x) = a\sin(b(x + c)) + d$.

Maximum: d + |a|. Minimum: d - |a|.

1. Substitute x, y, a, b, and d into $f(x) = a\sin(b(x + c)) + d$. 2. Solve for 'c'.

If 'a' is negative, the function is reflected over the x-axis.

1. Calculate amplitude and vertical shift. 2. Calculate 'b' from the period. 3. Determine the phase shift (if any). 4. Write the equation.

Half the distance between the maximum and minimum y-values. Calculated as $\frac{|max - min|}{2}$.

The horizontal distance required for the function to complete one full cycle.

Related to the period by $b = \frac{2\pi}{period}$, where 'b' is a parameter in the sinusoidal equation.

The vertical translation of the midline of the function. It's the 'd' value in the equation $f(x) = a\sin(b(x + c)) + d$.

The horizontal translation of the function, indicating how much the graph is shifted left or right.

The horizontal line that runs midway between the maximum and minimum values of the function. Calculated as $\frac{max + min}{2}$.

Amplitude.

Frequency, related to the period.

Horizontal shift (phase shift).

Vertical shift.

$f(x) = a \sin(b(x + c)) + d$

$f(x) = a \cos(b(x + c)) + d$

$amplitude = \frac{|max - min|}{2}$

$b = \frac{2\pi}{period}$

$d = \frac{max + min}{2}$

Period = $\frac{2\pi}{b}$, where b is frequency.

$midline = \frac{max + min}{2}$

$b = \frac{2\pi}{Period}$

$Period = \frac{2\pi}{b}$

$max = d + |a|$

$min = d - |a|$