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2 answers:
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Answer:
Area: 180 units2 (units 2 is because since the are no specific unit given but every area should have a unit of measurement)
Step-by-step explanation:
The area enclosed by the graph of the function, the horizontal axis, and vertical lines is the integral of the function between thos two points (x=2 and x=4)
So , let's solve the integral of f(x)
Area =+C
C=0
So if we evaluate this function in the given segment:
Area= 3* (4^4)/4-3*(2^4)/4= 3*(4^4-2^4)/4=180 units 2
Goos luck!
To find the equation of the graph, what we do is to recognize some characteristics of a sine function:
- Amplitude: The amplitude of the sine function is the distance from the middle value or line running through the graph up to the highest point. In this case, the amplitude is 1.
- Period: The period of a sine function is defined as the length of one complete sine wave or one complete cycle of the curve. It can be found using the equation: P=2pi/B.
Why are these characteristics important?
Because the sine function has the following general form:
In this problem, we have A=1 and we know that the period equals 2pi/3. So,
Therefore, the equation of the graph is:
- y=x³
Horizontally streched means change in x
So
New equation
- y=kx³
k is factor
- y=1/5x³
We know the rule for reflection (x,y)=(x,-y)
So
New function
- -y=1/5x³
- y=-1/5x³
Option D
