Question

Which of the following describes how the dotted line relates to the solid line (f(x))? reflection through the y-axis, f(x) → f(-x) reflection through the x-axis, f(x) → -f(x) reflection through the y-axis, f(x) → -f(x) reflection through the x-axis, f(x) → f(-x) | 100 POINTS|

Answer 1

Reflection through the x-axis, f(x) → -f(x).

Explanation:

On comparison of the dotted red line with the solid blue line, it is apparent that the x-coordinates do not change, yet the y-coordinates are negatives of each other.

This suggests a reflection in the x-axis.

(Note: If the function was reflected in the y-axis, the y-coordinates would not change, yet the x-coordinates would be negatives of each other).

Mapping rule for reflection in the x-axis:

• (x, y) → (x, -y)

Therefore, as y → -y then f(x) → -f(x).

So the correct answer that describes how the dotted line relates to the solid line f(x) is:

• Reflection through the x-axis, f(x) → -f(x).

Answer 2

• B) reflection through the x-axis, f(x) → -f(x)

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We observe on the graph that:

• The line is reflected across the horizontal axis, which is the x-axis,
• The reflection doesn't affect the x-coordinates,
• The reflection changes each y-coordinate to opposite sign.

All the above helps us to conclude that:

• This is the reflection through the x-axis, f(x) → -f(x)