Reflect Across The Y Axis

REFLECTION ACROSS THE Y-AXIS

A reflection can be done across the y-centrality by folding or flipping an object over the y axis.

The original object is called the pre-image , and the reflection is called the image . If the pre-prototype is labeled as ABC, then t he image is labeled using aprime symbol, such as A'B'C'.

An object and its reflection have the same shape and size , but the figures face in contrary directions. The objects appear as if they are mirror reflections, with right and left reversed.

Rule

Let y = f(x) be a role.

In the above function, if we want to do reflection across the y-axis, ten has to be replaced by -10 and nosotros get the new function

y = f(-10)

The graph of y = f(-x) can be obtained past reflecting the graph of y = f(x) across the y-axis.

It tin can be washed by using the rule given below.

That is, if each point of the pre-image is (x, y), then each betoken of the paradigm subsequently reflection over y-centrality will be

(-10, y)

Instance :

Do the following transformation to the part y = √x.

"A reflection across the y - centrality"

And also write the formula that gives the requested transformation and draw the graph of both the givenfunction and the transformed function

Solution :

Step one :

Since nosotros practise reflection transformation beyond the y-axis, we have to supersede x past -ten in the given function

y = √x

Footstep 2 :

So, the formula that gives the requested transformation is

y = √-x

Step 3 :

The graph y = √-x tin can be obtained by reflecting the graph of y = √10 across the y-axis using the rule given below.

(x, y)----> (-10, y)

Step 4 :

The graph of the original function (given part)

Step 5 :

The graph of the transformed function.

How to sketch the reflected graph across the y-centrality?

In the above function, we tin easily sketch the reflected graph across the y-centrality.

For some other functions, students may observe it hard to sketch the reflected graph.

For example, students may find it difficult to sketch the reflected prototype of the triangle whose vertices are

A(-2, ane), B(ii, 4) and C (four, ii)

To get the reflected image across the y-axis, they merely have to apply the rule

(x, y) ----> (-x, y)

in the above three vertices.

When they do so, they can get the vertices of the reflected image.

They are

A'(2, ane) , B'(-2, 4) and C'(-4, ii)

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