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3 years ago

What type of transformation takes the graph of f(x)=|x| to the graph of g(x)=−3+|x|?

Mathematics

2 answers:

timama [110]3 years ago

8 0

Answer:

vertical translation of 3 units down

Step-by-step explanation:

i took the quiz on k12

IRINA_888 [86]3 years ago

7 0

Answer:

vertical translation of 3 units down

Step-by-step explanation:

we have

$f\left(x\right)=\left|x\right|$

The vertex of the graph of f(x) is the point (0,0)

$g\left(x\right)=-3+\left|x\right|$

The vertex of the graph of g(x) is the point (0,-3)

see the attached figure to better understand the problem

The transformation of f(x) to g(x) is

f(x) -----> g(x)

(0,0) -----> (0,-3)

(x,y) -----> (x,y-3)

That means -----> The translation is 3 units down

therefore

vertical translation of 3 units down

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Step-by-step explanation:

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3 years ago

Find the coordinates of the circumcenter of △PQR with vertices P(−2,5), Q(4,1), and R(−2,−3).

mel-nik [20]

Answer: (1/3,2)

Step-by-step explanation:

Let O(x,y) be the circumference of the triangle PQR,

Thus, by the property of circumcenter all the vertices of the triangle are at same distance from this circumcenter.

Thus, PO = QO

By the distance formula,

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$\implies 4x + 4 + 25 - 10 y = 16 - 8 x + 1 - 2y$

$\implies 4x +8x-10y+2y = 16 + 1 -25-4$

$\implies 12x - 8y = 17 - 29$

$\implies 12 x - 8 y = - 12$ ---------(1)

Similarly, QO = RO

$\implies (x-4)^2 + (y-1)^2 = (x+2)^2+(y+3)^2$

$\implies x^2 + 16 - 8x + y^2+ 1 - 2y = x^2+ 4 + 4 x +y^2+ 9 + 6 y$

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By adding equation (1) and (2),

24 x = - 8

x = 1/3

By putting this value in equation (1),

We get,

Thus, 4 - 8 y = -12

8 y = 16

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3 years ago

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andriy [413]

Answer:

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But to find the nth term of a geometric sequence, use the formula

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r is the common ratio of the sequence.

Example: To find the nth term of the geometric sequence

1/2, 1/4, 1/8, 1/16, ...

Here, a = 1/2

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Sn = (1/2)(1/2)^( n - 1)

Apply this method to the sequence you were given, it will be helpful.

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