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3 years ago

F(x)=x^2 . what is g(x)? please help ‍♀️

Mathematics

1 answer:

blagie [28]3 years ago

7 0

Answer:

D) g(x) = 4x^2 because the given point works when it's plug in the equation.

Step-by-step explanation:

It's a vertical stretch so a>1 for the transformation

Definitely not C, since it's a shrink with 0<a<1.

Plug in the point to see which one works

g(x) = 16x^2

g(1) = 16. A is not right

B is the same thing to A

g(1) = (4*1)^2 = 16. So, B is also not right

For D:

g(1) = 4(1)^2 =4. Point (1,4) that's show on the graph works for this equation.

D is correct

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Given:

The vertices of a rectangle are E(4,8), F(2,8), G(2,-2) and H(-4,-2).

The rectangle is dilated with the origin as the center of dilation so that G's is located at (5,-5).

To find:

The algebraic representation that represents this dilation.

Solution:

If a figure is dilated by factor k with origin as the center of dilation, then the dilation is defined as:

$(x,y)\to (kx,ky)$ ...(i)

Let the given rectangle is dilated by factor k with origin as the center of dilation. Then,

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$G(2,-2)\to G'(2k,-2k)$

The image of G after dilation is G'(5,-5). So,

$(2k,-2k)=(5,-5)$

On comparing both sides, we get

$2k=5$

$k=\dfrac{5}{2}$

So, the scale factor is $k=\dfrac{5}{2}$ .

Substituting $k=\dfrac{5}{2}$ in (i), we get

$(x,y)\to \left(\dfrac{5}{2}x,\dfrac{5}{2}y\right)$

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