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joja [24]
3 years ago
10

Consider the functions. F(x)=(x+1)2-4 and g(x)=-4|x+1| which statement compares the range of the functions?

Mathematics
1 answer:
Andreyy893 years ago
3 0

Answer:

<h2>        The fourth</h2>

Step-by-step explanation:

Vertex of f is (-1, -4) so its range is limited to y≥-4

|x+1| is always ≥0 therefore -|x+1| is always ≤0 {4 is insignificant to this - slope doesn't mean in range} so its range is limited to y≤0

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Y-intercept = (0, 2)<br> slope = -3/7 what is the equation?
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(see attached)

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ABC was dilated to create A' B' C'. What is the center of dilation? And what is the scale factor of the dilation?
Virty [35]

Given:

In the given figure the vertices of triangle ABC are A(-2,2), B(4,2), C(-2,-2).

The vertices of triangle A'B'C' are A'(-4,4), B'(8,4), C'(-4,-4).

To find:

The center of dilation and the scale factor.

Solution:

In the given graph, draw the lines AA', BB' and CC'. The intersection point of these lines is the center of dilation.

From the below graph, it is clear that the lines AA', BB' and CC' intersect each other at (0,0).

Therefore, the center of dilation is (0,0).

If a figure is dilated by factor k and the center of dilation is origin, then

(x,y)\to (kx,ky)

A(-2,2)\to A'(k(-2),k(2))

A(-2,2)\to A'(-2k,2k)

It is given that A'(-4,4). So,

(-2k,2k)=(-4,4)

On comparing both sides, we get

-2k=-4

2k=4

k=\dfrac{4}{2}

k=2

Therefore, the scale factor is 2.

4 0
3 years ago
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