In order to find average rate of change over an interval, do the y2-y1/x2-x1. Solve y for x=9 and x= 4
y2 = -3(9-4)^2 + 3 = -72
y1 = -3(4-4)^2 + 3 = 3
Now, x2 matches with y2 and and x1 matches with y1 obviously...
-72 - 3/9 - 4 = -15
An example of a trig function that includes multiple transformations and how it is different from the standard trig function is; As detailed below
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How to interpret trigonometric functions in transformations?</h3>
An example of a trigonometric function that includes multiple transformations is; f(x) = 3tan(x - 4) + 3
This is different from the standard function, f(x) = tan x because it has a vertical stretch of 3 units and a horizontal translation to the right by 4 units, and a vertical translation upwards by 3.
Another way to look at it is by;
Let us use the function f(x) = sin x.
Thus, the new function would be written as;
g(x) = sin (x - π/2), and this gives us;
g(x) = sin x cos π/2 - (cos x sin π/2) = -cos x
This will make a graph by shifting the graph of sin x π/2 units to the right side.
Now, shifting the graph of sin xπ/2 units to the left gives;
h(x) = sin (x + π/2/2)
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Answer:
B becauae of the other awnser not adding up
The given line is y = 3x - 5 after adding Y and subtracting 5 from both sides.
The slope of this given line is 3.
Therefore, the slope of the perpendicular line is -1/3, as it must be the negative reciprocal.
The general form of a line equation in slope intercept form is y = Mx+B where M is the slope and B is the intercept.
Solving for B is: B = y- Mx
So the intercept of the perpendicular line with slope M=-1/3 and passing through (x=4, y=-3) is
y M * x
B = -3 - (-1/3)*4 =
-3 + 1/3*4 = <-- subtracting the negative is the same as adding the positive; definition of subtraction
-3 + 4/3 = <-- multiplies the fractions first per order of mixed operations
-9/3 + 4/3 <-- common denominator is 3
= -5/3
So the equation of the perpendicular line is y = -1/3X + -5/3 = -1/3X-5/3
Notice when X=4, y = -1/3(4) - 5/3 = -4/3 - 5/3 = -9/3 = -3 as expected
Answer:
C 2
Step-by-step explanation:
This is a parabolic function
Notice how we go negative and then positive
y = ax^2 +bx+c
Let x = 0
-5 = a(0) + b(0) +c
c = -5
y = ax^2 + bx -5
Let x = 3
4 = a(3)^2 +b(3) -5
Let x=-3
4 = a(3)^2 -b(3) -5
Add the two equations
4 = a(3)^2 +b(3) -5
4 = a(3)^2 -b(3) -5
----------------------------
8 = 2a (3)^2 - 10
18 = 2 a(9)
18 = 18a
a =1
Solving for b
4 = 1(3)^2 -b(3) -5
4 = 9 -3b -5
4 = 4 -3b
0 = -3b
0 =b
The equation is
y = (x)^2 -5
Letting y = -1
-1 =x^2 -5
Adding 5 to each side
4 = x^2
Taking the square root of each side
±2 = x
x= ±2
Given the choices
