Find g(x), where g(x) is the reflection across the x-axis of f(x) = x?.

Mathematics

1 answer:

nignag [31]3 years ago

6 0

Answer:

$g(x) = -x$

Step-by-step explanation:

The reflection of a function $f(x)$ along the $x - axis$ is given by $g(x) = -f(x)$ .

Here the given function is $f(x) = x$ . Therefore the reflection would be $g(x) = -x$ .

To find reflection draw the graph of it and think about how the graph of its mirror image would be. You would arrive at the reflection function.

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Answer:

Part A

The rotation of the point (x, y) 180° about the origin gives the point (-x, -y)

Therefore, we have the points, ΔLMN, L(1, 1), and M(2, 2), and N(3, 3)

The coordinates of the vertices of the image, ΔL'M'N' are L'(-1, -1), and M'(-2, -2), and N'(-3, -3)

Please find attached the graph of triangle ΔLMN and ΔL'M'N'

Part B

The lines drawn through L and L' and through M and M' are colinear

Part C

A line is defined by two points, such as L and M. Rotation of a line through 180° about the origin will give an image location on the same path as the extension of the original line.

The third point, N, however, defines a plane, and the rotation of a plane by 180° will give an image which is turned upside down with regards to the preimage

Therefore, a trough in the preimage becomes a peak in the image and the lines drawn through N and N' crosses the colinear lines drawn throgh M and M' and L and L'

Step-by-step explanation: