The parent function f(x) = x3 is transformed to g(x) = (x – 1)3 + 4. Identify the graph of g(x).
2 answers:
Answer:
The graph of g(x) will be shifted 4 units up and 1 unit to the right
Step-by-step explanation:
The parent function f(x) = x^3 is transformed to g(x) = (x – 1)^3 + 4
Parent function f(x)= x^3
If any number is added at the end then the graph will be shifted up
If any number is subtracted from x then graph will be shifted right
f(x)----> f(x) + a (shifted 'a' units up)
f(x) ----> f(x-a) (shifted 'a' units right)
g(x) = (x – 1)^3 + 4
The graph of g(x) will be shifted 4 units up and 1 unit to the right
the graph is attached below
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Answer with explanation:
It is given that , ride at an amusement park moves the riders in a circle at a rate of 6.0 m/s.
Radius of Circle = 9.0 meters
Acceleration is rate of change of velocity,which will be perpendicular to radius vector.
Also, in terms of mathematics, line from center that is radius , to point of contact that is tangent line ,which is on the circle are perpendicular to each another.
→r(radius vector) ⊥ a(Acceleration vector).
So, In option A, Radius vector is Perpendicular to acceleration of riders.
Answer:
Step-by-step explanation:
Since you did not indicate what you need to do, I assume that you have to write an expression using the sentence given in the problem.
In order to solve this exercise, it is importat to remember the following information:
1. The quotient is the result of a division.
2. The sum is the result of an addition.
3. The word "twice" indicates a multiplicatio by 2.
4. The word "cube" indicates an exponent 3.
Then, keeping on mind the explained above and the data given in the exercise, you know that:
-The sum of and
can be expressed as:
- Twice the cube of can be expressed in the following form:
Therefore, you can dermine that "the quotient of the sum of and
and twice the cube of
" is represented with the following expression:
O
The given <span>expression is 
</span>
So, we have 3 square roots.
The number under a square root sign must be Non negative.
Beside that the denominator must be not equal zero.
For the term ⇒⇒⇒
∴ x > 0 ⇒⇒⇒ x ∈ (0,∞)
For the term ⇒⇒⇒
∴x+1 ≥ 0 ⇒⇒⇒ x ≥ -1 ⇒⇒⇒ ∴ x ∈ [-1,∞)
For the term ⇒⇒⇒
∴ 1-x ≥ 0 ⇒⇒⇒ x ≤ 1 ⇒⇒⇒ x ∈ (-∞,1]
So, The values of x which make the <span>expression well defined
</span>
<span>∴ x ∈ { </span><span>(0,∞) ∪ </span><span>[-1,∞) ∪ </span><span>(-∞,1] }
</span><span>
</span><span>∴ x ∈ [-1,0) ∪ (0,1]
</span><span>
</span><span>OR can be written as ⇒⇒ x ∈ [-1,1] - {0}
</span>
</span>
So, we have 3 square roots.
The number under a square root sign must be Non negative.
Beside that the denominator must be not equal zero.
For the term ⇒⇒⇒
∴ x > 0 ⇒⇒⇒ x ∈ (0,∞)
For the term ⇒⇒⇒
∴x+1 ≥ 0 ⇒⇒⇒ x ≥ -1 ⇒⇒⇒ ∴ x ∈ [-1,∞)
For the term ⇒⇒⇒
∴ 1-x ≥ 0 ⇒⇒⇒ x ≤ 1 ⇒⇒⇒ x ∈ (-∞,1]
So, The values of x which make the <span>expression well defined
</span>
<span>∴ x ∈ { </span><span>(0,∞) ∪ </span><span>[-1,∞) ∪ </span><span>(-∞,1] }
</span><span>
</span><span>∴ x ∈ [-1,0) ∪ (0,1]
</span><span>
</span><span>OR can be written as ⇒⇒ x ∈ [-1,1] - {0}
</span>