Question

An ant moves along the curve whose equation is f(x) = x^2+ 1 in the restricted domain [0,infinity)Let a mirror
be placed along the line y = x. If the reflection of the ant with respect to the mirror moves along the curve g(x), then
which of the following options is(are) correct?

Answer 1

Answer:

$g(x) = f(x)$

Answer 2

Answer:

The reflection of the ant with respect to the mirror gives $g(x)=f(x)$

Step-by-step explanation:

Transformation: A parent function can be transformed into a similar function, using reflection.

Reflection can be done in two ways: horizontal and vertical.

• A horizontal reflection reflects the graph over the y-axis.
• Here, the y-values remain the same but the x-values will get opposite sign, given by $g(x)=f(-x)$.
• A vertical reflection reflects the graph over the x-axis.
• Here, the x-values remain the same whereas the y-values will have the opposite sign, given by .$g(x)=-f(x)$

Given a function, $f(x) = x^2+ 1$

And a mirror is placed along the line $y=x$, so its a horizontal reflection.

In horizontal reflection, the input x-values will get opposite sign.

Therefore,

$g(x)=f(-x) = (-x)^2+ 1=x^2+ 1=f(x)$

Therefore, the reflection of the ant with respect to the mirror gives $g(x)=f(x)$.

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