1) Considering the parent function: f(x) = sin(x) and the function g(x)=5sin(-2x) +2
We have the following information:
g(x)=5sin(-2x) +2
Amplitude, to find that out in any function y= a.bsin(bx-c)+d the absolute value of A is the amplitude. So in this case the Amplitude is 5
Graphically
Note the midline in purple, the g(x) in green, and f(x) in blue.
• Frequency
Frequency Is the number of cycles on a certain interval. Algebraically we can find it through a formula
[tex]f=\frac{b}{2\pi}\Rightarrow f=\frac{-2}{2\pi}=\frac{1}{\pi}[/tex]
• Period
A period marks the distance between a trig function starts to behave the same.
Algebraically is found by:
[tex]P=\frac{2\pi}{|b|}=\frac{2\pi}{|-2|}=\pi[/tex]
• Phase Shift
Phase shift, by definition, is the distance a trigonometric function is shifted horizontally. Algebraically, is found by:
[tex]\begin{gathered} Phase=\frac{c}{b}=\frac{0}{2}=0 \\ Vertical\colon\text{ d=2} \end{gathered}[/tex]
• Vertical Translation:
Since there are no Vertical asymptotes, we can state that the vertical translation doesn't exist.
• Midline
The midline of a trigonometric function marks using a horizontal line the central point where the curve oscillates. The midline is found by the vertical translation, in this case, y=2
