the equation (y-3)^2 =4y-12
y = -7
Answer:
left 1 unit, reflection about the x-axis, up 1 unit
Step-by-step explanation:
This is a cubic that has been moved left 1 unit because of the (x+1)^3 part.
It also has been moved up one unit because of the plus 1 on the outside of the cube.
There has also been a reflection across the x-axis because of the -1 in front of the -(x+1)^3 part.
In general, g(x-h)+k means:
1) the function g has been moved right (if h is positive) or moved left (if h is negative).
2) the function g has been moved up (if k is positive) or down (if k is negative)
Answer: 1/3 (x + 6)
Explanation: given f(x) = 3x - 6.
Let y = f(x) and so y = 3x - 6.
Trade places between x and y.
x = 3y - 6
Solve for y
x + 6 = 3y
y = x + 6/3
Now the new y is the inverse and so y = f-1(x)
f-1(x) = 1/3(x + 6)
Basically, you just move every individual point up, down, left, or right by the amount indicated.
For example, point G is graphed on the point (-3, -1). Moving it right 5 and up 1 will give you G’, which is (2,0)
T is graphed on the point (-1, -1). Moving it right 5 and up 1 will give you T’, which is (4,0)
B is graphed on the point (-3, -5). Moving it right 5 and up 1 will give you B’, which is
(2,4)
When x=0,
y=-(0-2)^3-5
y=3
When y=0,
(x-2)^3=5
x-2= +/- 5^1/3
x= +/- 5^1/3 +2
x= 3.70997 or x=0.29002
To find the turning point at y, substitute the information that you have found above.
y=-(3.70997-2)^3-5
y=-9.99994
Find the mid-point next as mid-point is also the turning point.
(3.70997+0.29002)÷2=1.999995
Hence, Turning point is (1.999995, 9.99994)
Plot a graph using turning point, y value and the 2-x values.
