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AleksAgata [21]
3 years ago
12

Which translation maps the graph of the function f(x) = x2 onto the function g(x) = x2 + 2x + 6?

Mathematics
2 answers:
Flura [38]3 years ago
4 0
The graph went left 1 and up 6. You could complete the square to find out or just graph it!
Hope this helps!
Shtirlitz [24]3 years ago
4 0

Answer:

Translation: Shift 1 unit left and 5 unit up

Step-by-step explanation:

Given: f(x)=x^2

Translation function, g(x)=x^2+2x+6

First we change g(x) into vertex form and then check the translation.

g(x)=x^2+2x+6

Completing square

g(x)=(x^2+2x+1)+5

g(x)=(x+1)^2+5                     \because a^2+2ab+b^2=(a+b)^2

Now, we will compare the function with f(x)

f(x)=x^2

Shift f(x) 1 unit left

f(x)=(x+1)^2

Shift f(x) 5 unit up

f(x)=(x+1)^2+5=g(x)

Translation: 1 unit left and 5 unit up

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Answer:

A'(-2, 1), B'(1, 0), C'(-1, 0)

Step-by-step explanation:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, dilation and translation.

If a point X(x, y) is translated a units right and b units down, the new location is X'(x + a, y + b) whereas if a point X(x, y) is translated a units left and b units up, the new location is X'(x - a, y - b).

If a point X(x, y) is rotated 90° clockwise about the origin, the new location is X'(y, -x)

From the image attached, ∆ABC is at A(0, 0), B(1,3) C(1, 1)

If ∆ABC is translated 2 units down and 1 unit to the left (x - 1, y - 2), the vertices would be A*(-1, -2), B*(0, 1), C*(0, -1)

If it is then rotated 90° clockwise about the origin, the new location is A'(-2, 1), B'(1, 0), C'(-1, 0)

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Write a function for the tranformations described below:
IrinaK [193]

The function after the transformation has an equation of y = ∛(x - 7) + 5

<h3>How to determine the equation of the transformation?</h3>

The transformation statement is given as

"The cubic function shifts 7 units right and 5 units up."

A cubic function is represented as

y = ∛x

So, the transformations are:

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Mathematically, this can be represented as

(x, y) = (x - 7, y + 5)

So, we have the following equation

y = ∛(x - 7) + 5

Hence, the equation of the transformation is y = ∛(x - 7) + 5

Read more about transformation at

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Step-by-step explanation:

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<em><u>The recursive formula to find nth term of sequence is:</u></em>

a_n = 4n - 1 \text{ where } n \geq 1 and n  = 1, 2, 3, ....

<em><u>Solution:</u></em>

Given a sequence is:

3, 7, 11, 15, 19, 23, 27, 31, 35

<em><u>Let us find the difference between terms</u></em>

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11 - 7 = 4

15 - 11 = 4

19 - 15 = 4

23 - 19 = 4

27 - 23 = 4

31 - 27 = 4

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Thus the difference between terms is constant

Thus the given sequence is arithmetic sequence

An arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant

<em><u>The nth term of arithmetic sequence is given by:</u></em>

a_n =a_1+(n-1)d

a_n = the nᵗʰ term in the sequence

a_1 = the first term in the sequence

d = the common difference between terms

Here in the given sequence

d = 4

a_1=3

Substitute in above formula,

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