Horizontal translations of functions are the transformations that shifts the original graph of the function either to the right side or left side by some units.

A horizontal translation "slides" an object a fixed distance either on the right side or left side. The original object and its translation have the same shape and size, and they face in the same direction.

In simple words, horizontal translation means, it just moves the given figure either on the right or left without rotating, re-sizing or anything else.

Let y = f(x) be a function and "k" be a constant.

In the above function, if "x" is replaced by "x-k" , we get the new function

y = f(x - k)

The graph of y = f(x-k) can be obtained by the translating the graph of y = f(x) to the right by "k" units if "k" is a positive number.

In case "k" is a negative number, the graph of y = f(x) will be translated to the left by |k| units.

Moreover, if the the point (x,y) is on the graph of

y = f(x),

then the point (x+k , y) is on the graph

y = f(x - k)

For example, if k = 3, the graph of y = f(x) will be translated to the right by "3" units.

If k = -3, the graph of y = f(x) will be translated to the left by "3" units.

**Example :**

Perform the following transformation to the function

y = √x.

"a translation to the right by 3 units"

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

**Answer :**

**Step 1 :**

Since we do a translation to the right by "3" units, we have to replace "x" by "x-3" in the given function

y = √x

**Step 2 :**

So, the formula that gives the requested transformation is

y = √(x-3)

**Step 3 :**

The graph y = √(x-3) can be obtained by translating the graph of y = √x to the right by "3" units.

**Step 4 :**

The graph of the original function (given function)

**Step 5 : **

The graph of the transformed function.

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

If you have any feedback about our math content, please mail us :

**v4formath@gmail.com**

We always appreciate your feedback.

You can also visit the following web pages on different stuff in math.

**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**

**Trigonometry 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**