I need help with finding the limit for problem #1. I've already solved 2-4 I just don't get the first one.

Mathematics

1 answer:

emmainna [20.7K]2 years ago

7 0

Answer: 9

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Look at the graph of f(x). Locate x = 3 on the graph and move to the left of that location. If you get closer and closer to x = 3 from the left side, then you approach y = 3

Do the same for g(x) as well. If you approach x = 3 from the left, then you approach y = 3. It does not matter there is a discontinuity here as we're only worried about approaching x = 3 from the left and not actually getting to that specific x value.

We multiply those y values to get 3*3 = 9 as the answer

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atroni [7]

By applying the equation of dilation, the coordinates of the vertices of the triangle ABC are A'(x, y) = (-12, 0), B'(x, y) = (0, -9) and C'(x, y) = (-12, -9).

<h3>How to find the image of a triangle</h3>

A dilation is a type of rigid transformation. Rigid transformations are transformations applied to geometric loci such that Euclidean distances are conserved.

There is a triangle and its image must be a triangle, the new triangle is found by transforming the three vertices of the prior one following this formula:

A'(x, y) = P(x, y) + k · [A(x, y) - P(x, y)] (1)

Where:

P(x, y) - Center of reflection.
A(x, y) - Original vertex
A'(x, y) - New vertex
k - Dilation factor

If we know that P(x, y) = (0, 0), A(x, y) = (-4, 0), B(x, y) = (0, -3) and C(x, y) = (-4, -3), then the new vertices of the triangle are, respectively:

Point A

A'(x, y) = (0, 0) + 3 · [(-4, 0) - (0, 0)]

A'(x, y) = (-12, 0)

Point B

B'(x, y) = (0, 0) + 3 · [(0, -3) - (0, 0)]

B'(x, y) = (0, -9)

Point C

C'(x, y) = (0, 0) + 3 · [(-4, -3) - (0, 0)]

C'(x, y) = (-12, -9)

Lastly, we draw the two triangles, which are presented in the image attached below.

To learn more on dilations: brainly.com/question/13176891

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