QQuestionMathematics
QuestionMathematics
Which answer shows a reflection across the x-axis?
# 2014
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Answer
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Step 1:: Identify the given graph
The given graph shows a parabola opening upwards. The equation of this parabola is not provided, but we can still determine the reflection of this graph across the x-axis without knowing its equation.
Step 2:: Understand the transformation
Reflecting a graph across the x-axis results in a point-by-point transformation where each y-coordinate changes sign while the x-coordinates remain the same. In other words, (x, y) becomes (x, -y) after the reflection.
Step 3:: Visualize the reflected graph
To visualize the reflected graph, consider any point on the given graph and change its y-coordinate sign. For example, if we take the point (2, 1) from the original graph, the reflected point will be (2, - 1). By doing this for all points on the graph, we obtain the reflected graph, which is also a parabola opening downwards.
Step 4:: Find the corresponding answer choice
Now, we need to find the answer choice that represents the reflected graph. By comparing the given options with our visualization, we can see that option B shows the reflection across the x-axis.
Final Answer
Option B shows a reflection across the x-axis.
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