Mathematics, 29.01.2020 00:51 ari758540

Which of the following is an even function g(x) = (x – 1)2 + 1g(x) = 2x2 + 1g(x) = 4x + 2g(x) = 2x

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An even function can be reflected about the y axis and map onto itself
example: y=x^2

an odd function can be reflected about the origin and map onto itself
example: y=x^3

a simple test is the following

if f(x) is even then f(-x)=f(x)
if f(x) is odd then f(-x)=-f(x)

so

even function
subsitute -x for each and see if we get the same function
remember to fully expand these

g(x)=(x-1)^2+1=x^2-2x+1+1=x^2-2x+2 is the original one

g(x)=(x-1)^2+1
g(-x)=(-x-1)^2+1
g(-x)=(1)(x+1)^2+1
g(-x)=x^2+2x+1+1
g(-x)=x^2+2x+2
not same because the original has -2x
not even

g(x)=2x^2+1
g(-x)=2(-x)^2+1
g(-x)=2x^2+1
same, it's even

g(x)=4x+2
g(-x)=4(-x)+2
g(-x)=-4x+2
not the same, not even

g(x)=2x
g(-x)=2(-x)
g(-x)=-2x
not same, not even

g(x)=2x²+1 is the even function

Answer from: jm900643

2nd function is even function.

Step-by-step explanation:

Given Functions are

$1.\: g(x)=(x-1)^2+1\\2.\:g(x)=2.x^2+1\\3.\:g(x)=4.x+2\\4.\:g(x)=2.x$

Even Functions are functions whose value didnt change if we replace the variable with negative of the variable.i.e., f(x) = f(-x)

here,

1st function

$g(x)=(x-1)^2+1\implies g(x)= x^2-2.x+1+1\implies g(x)=x^2-2.x+2$

replacing x by -x we get

$g(-x)=(-x)^2-2.(-x)+2\\g(-x)=x^2+2.x+2\\\implies g(-x)\neq g(x)$

∴ It is not an even function.

2nd function

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

replacing x by -x we get,

$g(-x)=2.(-x)^2+1\\g(-x)=2.x^2+1\\\implies g(-x)=g(x)$

∴It is an even function.

3rd function

g(x)=4.x+2

replacing x by -x we get,

$g(-x)=4.(-x)+2\\g(-x)=-4.x+2\\\implies g(-x)\neq g(x)$

∴It is not an even function

4th function

g(x)=2.x

replacing x by -x we get,

$g(-x)=2.(-x)\\g(-x)=-2.x\\\implies g(-x)\neq g(x)$

∴It is not an even function

Therefore, only 2nd function is even function.

Answer from: Quest

use formula for the circle a=3.14

step-by-step explanation:

Answer from: Quest

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation:

Identify the transformation that maps the figure with center (7, 1) onto itself. a) rotate 180° cloc

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Which of the following is an even function g(x) = (x – 1)2 + 1g(x) = 2x2 + 1g(x) = 4x + 2g(x) = 2x...

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