Which of the following transformations of f(x) = | x | has no effect on its graph? A) Reflection over the y-axis
B) Reflection over y = x
C) Reflection over y = -x
D) Reflection over the x-axis

A) Reflection over the y-axis

Step-by-step explanation:

The graph is given as : f(x) = | x |

As attached, the graph open upwards originating from the origin.

A reflection on the y-axis will map the points on the right to points on the left. For example, a point (4,4) will map to point  (-4,4) and vice versa to maintain the same graph with no effect.

Answer choice B is incorrect in that a point   (-2,2) will be mapped to  (2,-2) which has an effect on the -ve sign which will shift from the x-coordinate to the y coordinate.

Answer choice C is incorrect because a point (2,2)  will be mapped to a point (-2,-2) which has an effect in that the transformation has introduced a  -ve sign in its object coordinates for the image coordinates.

Answer choice D is incorrect because the graph formed for the image will open downwards unlike the graph for the object.

answer for #1 is c

answer for #2 is d

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