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umka2103 [35]
2 years ago
9

How does the graph of g(x) = (x − 1)3 + 5 compare to the parent function f(x) = x3?

Mathematics
1 answer:
ser-zykov [4K]2 years ago
5 0

Answer:

The original function was transformed by a a horizontal shift to the right in 1 unit, and also a vertical shift upwards of 5 units.

Step-by-step explanation:

Recall the four very important rules regarding translations (shifts) of the graph of functions:

1) In order to shift the graph of a function vertically c units upwards, we must transform  f (x) by adding c to it.

2) In order to shift the graph of a function vertically c units downwards, we must transform  f (x) by subtracting c from it.

3) In order to shift the graph of a function horizontally c units to the right, we must transform the variable x by subtracting c from x.

4) In order to shift the graph of a function horizontally c units to the left, we must transform the variable x by adding c to x.

We notice that in our case, The original function f(x)=x^3 has been transformed by "subtracting 1 unit from x", and by adding 5 units to the full function. Therefore we are in the presence of a horizontal shift to the right in 1 unit (as explained in rule 3), and also a vertical shift upwards of 5 units (as explained in rule 1).

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31. Algebra Fill in the reason that justifies each step.
Anna11 [10]

Answer:

Step-by-step explanation:

<u>Statements    </u>                                   <u>  Reasons</u>

1) QS =42                                               Given

2) QR + RS = QS                              Segment Addition Postulate

3) (x + 3) + 2x = 42                            Substitution Property

4) 3x + 3 = 42                                      Simplify

5) 3x = 39                                          Subtraction Property of Equality

6) x=13                                               Division Property of Equality

Explanation:

We have given QS=42. We have to prove that x=13

We will use Segment Addition Postulate which states that given 2 points Q and S, a third point R lies on the line segment QS  if and only if the distances between the points satisfy the equation QR + RS = QS.

Then we will substitute the values in the defined postulate.

where QR= x+3

RS=2x

QS=42

QR+RS=QS

(x+3)+2x= 42

Now simplify the expression by opening the brackets.

x+3+2x=42

3x+3=42

Now subtract 3 from both sides.

3x+3-3=42-3

3x=39

divide both sides by 3.

3x/3 =39/3

x=13..

4 0
3 years ago
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Step-by-step explanation:

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Answer:

Step-by-step explanation:

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3 years ago
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