Answer:
f(x): Amplitude = 2, Period = 2
g(x): Amplitude = ¹/₂, Period = π
Step-by-step explanation:
The cosine function is periodic, meaning it repeats forever.
Standard form of a cosine function:
f(x) = A cos(B(x + C)) + D
where:
- A = amplitude (height from the mid-line to the peak)
- 2π/B = period (horizontal distance between consecutive peaks)
- C = phase shift (horizontal shift - positive is to the left)
- D = vertical shift
Function f(x)
[tex]f(x)=2 \cos (\pi x)[/tex]
Comparing this with the standard form of a cosine function:
- [tex]\sf Period = \dfrac{2 \pi}{\pi}=2[/tex]
Function g(x)
[tex]g(x)=\dfrac{1}{2} \cos (2x)[/tex]
Comparing this with the standard form of a cosine function:
- [tex]\sf Amplitude=\dfrac{1}{2}[/tex]
- [tex]\sf Period = \dfrac{2 \pi}{2}=\pi[/tex]
Learn more about the cosine graph here:
https://brainly.com/question/27818219
