"Reflection through x axis" is one of the different types of transformations of functions.

Even though students can get this stuff on internet, they do not understand exactly what has been explained.

To
make the students to understand the stuff "Reflection through x-axis",
we have explained the rule that we apply to make reflection
transformation through x-axis of a function.

Let **y = f(x)** be a function.

In the above function, if we want to do reflection through the x-axis, **"y"** has to be replaced by **"-y"** and we get the new function

-**y = f(x) **** **

**-y = f(x)** can also be written as **y = -f(x)**

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

It can be done by using the rule given below.

Once students understand the above mentioned rule which they have to apply for reflection through x axis, they can easily do this kind of transformations of functions.

Let us consider the following example to have better understanding of reflection through x axis.

**Question : **

Perform the following transformation to the function y = √x.

"a reflection through the x - axis"

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

**Solution: **

**Step 1 : **

Since we do reflection transformation through the x-axis, we have to replace "y" by "-y" in the given function y = √x.

**Step 2 : **

So, the formula that gives the requested transformation is

- y = √x or y = - √x

**Step 3 : **

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

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

**Step 4 : **

The graph of the original function (given function)

**Step 5 : **

The graph of the transformed function.

In the above function, we can easily sketch the reflected graph through the x-axis.

For some other functions, students may find it difficult to sketch the reflected graph.

For example, students may find it difficult to sketch the reflected image of the triangle whose vertices are A ( -2, 1), B (2, 4) and C (4, 2)

To get the reflected image through the x-axis, they just 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, -1) , B' ( 2, -4 ) and C' ( 4, -2) **

After having gone through the stuff given above, we hope that the students would have understood "Reflection through x axis".

Apart from the stuff given above, if you want to know more about "Reflection over x axis", please click here

If you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**

**Sum of all three four digit numbers formed using 0, 1, 2, 3**

**Sum of all three four digit numbers formed using 1, 2, 5, 6**