Mathematics, 30.06.2019 15:00 mariasoledad1

The graph of f(x) = x2 is translated to form g(x) = (x – 5)2 + 1.which graph represents g(x)?

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Answer from: cherryy

The graph of f(x)=x^2 and the graph of g(x)=(x-5)^2+1 . These two graphs are illustrated in the Figure bellow. So, let's explain what this means:

For a function f(x), a new function g(x) = f(x - c) represents to shift the graph c units to the right.For a function f(x), a new function g(x) = f(x) + k represents to shift the graph k units upward.

Since in our problem the function g(x) = f(x - c) + k, we have shifted the function f(x) c units to the right and k units upward, that is, we have shifted the function f(x) 5 units to the right and 1 unit upward as indicated in the Figure bellow.

The graph of f(x) = x2 is translated to form g(x) = (x – 5)2 + 1.which graph represents g(x)?

Answer from: twentyonepilots12018

The graph of the original function and the translated function can be seen at the end of the answer.

How do translations work?

There are two types of translations:

Vertical translation:

For a general function f(x), a vertical translation of N units is written as:

g(x) = f(x) + N.

If N is positive, then the shift is upwards.If N is negative, then the shift is downwards.

Horizontal translation:

For a general function f(x), a horizontal translation of N units is written as:

g(x) = f(x + N).

If N is positive, then the shift is to the left.If N is negative, then the shift is to the right.

Then if we go from:

f(x) = x^2

to:

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

Then we have a translation of 5 units to the right and one unit upwards.

The graph can be seen below.

If you want to learn more about translations, you can read:

link

Answer from: Quest

last option: rhombus or kite

step-by-step explanation:

a kite and rhombus have the same shape. as we don't have any specific formula for the calculation of area of kite. the diagonals are used to calculate the area of a kite or rhombus.

the formula for area of rhombus is given by:

$a = \frac{1}{2}d_{1} d_{2}$

here, d_1 is the first diagonal and d_2 is the second diagonal.

so,

last option is the correct answer ..

Answer for 15 points (look at the image)

Answer from: Quest

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