Questions: Where is the graph increasing and decreasing?

Where is the graph increasing and decreasing?
Transcript text: Where is the graph increasing and decreasing?
failed

Solution

failed
failed

Solution Steps

Step 1: Identify the function type

The graph appears to be a sinusoidal function, likely a sine or cosine function, given its periodic nature and the presence of maximum and minimum points.

Step 2: Determine the amplitude

The maximum value of the function is 8 and the minimum value is -8. The amplitude AA is half the distance between the maximum and minimum values: A=8(8)2=8 A = \frac{8 - (-8)}{2} = 8

Step 3: Determine the period

The period TT is the distance between two consecutive points where the function repeats its pattern. From the graph, the function repeats every 2π2\pi units along the x-axis.

Final Answer

The function is of the form y=Asin(Bx) y = A \sin(Bx) or y=Acos(Bx) y = A \cos(Bx) . Given the amplitude A=8A = 8 and the period T=2πT = 2\pi, we have B=2πT=1B = \frac{2\pi}{T} = 1. Therefore, the function can be written as: y=8sin(x) y = 8 \sin(x) or y=8cos(x) y = 8 \cos(x) .

Was this solution helpful?
failed
Unhelpful
failed
Helpful