Answer:
Step-by-step explanation:
We
Answer:
A function f(x) is said to be periodic, if there exists a positive real number T such that f(x+T) = f(x).
You can also just say: A periodic function is one that repeats itself in regular intervals.
Step-by-step explanation:
The smallest value of T is called the period of the function.
Note: If the value of T is independent of x then f(x) is periodic, and if T is dependent, then f(x) is non-periodic.
For example, here's the graph of sin x. [REFER TO PICTURE BELOW]
Sin x is a periodic function with period 2π because sin(x+2π)=sinx
Other examples of periodic functions are all trigonometric ratios, fractional x (Denoted by {x} which has period 1) and others.
In order to determine the period of the determined graph however, just know that the period of the sine curve is the length of one cycle of the curve. The natural period of the sine curve is 2π. So, a coefficient of b=1 is equivalent to a period of 2π. To get the period of the sine curve for any coefficient b, just divide 2π by the coefficient b to get the new period of the curve.
Hopefully this helped a bit.
Answer:
D: 2y = 8x - 10
Step-by-step explanation:
A: y = 4x + 5. This has a slope of -4 Yes it could work.
B: y = 4x - 5. No It does not work
C: 2y = 8x - 10. The slope is 8/2 = 4. So No it could not work.
<u>D: -2y = 8x - 10. The slope is 8/-2 = -4. Yes This Does work! :)</u>
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Answer:
Below
Step-by-step explanation:
First we can go ahead and create a general equation for this polynomial
Here are our roots :
x1 = - 3
x2 = -1
x3 = 1
Now because this function extends from quadrant 4 to 3, we know that this has been reflected in the x-axis :
f(x) = - ( x + 3 ) ( x + 1 ) ( x - 1 )
However if we look closely you can see that the graph appears to "bounce" off certain roots. In this case it bounces off x = 1. This means that this root is an order of 2. It also has a weird looking curve on x = - 3 which means that this root is an order of 3.
Our general equation will look like this :
f(x) = - ( x + 3 )^3 ( x - 1 )^2 ( x + 1 )
Now we need to sub in any point on the graph to solve for the <em>a </em>value. I'm just going to arbitrarily pick the y-intercept at ( 0 , -3 )
- 3 = - a ( 0 + 3 )^3 ( 0 - 1 )^2 ( 0 + 1 )
- 3 = - a (3)^3 (-1)^2 (1)
- 3 = - a (27)(1)(1)
- 3 = - a27
1/9 = a
Here is our FINAL equation :
f(x) = - 1/9 ( x + 3 )^3 ( x - 1 )^2 ( x + 1 )
Hope this helps! Best of luck <3
I would really appreciate a brainliest if possible :)
