**Using transformations to graph functions of the form y = af[k(x-d)] + c :**

In mathematics, we will have situation to graph a function from the parent function using transformation.

Here, we are going to see, how to graph the functions which are in the form y = af[k(x-d)] + c using transformation.

let us see, how to graph the functions which are in the form y = af[k(x-d)] + c using transformation with an example.

**Example : **

Sketch the graph of the function given below.

**Solution :**

The function is a transformed square root function.

So, the parent function is y = √x

Let us look at each part of the function and write down all the transformations which we need to apply.

First, let us divide the x- coordinates of points on y = √x by 2 to compress the graph horizontally by the factor 1/2.

When we do as said above, we will get the following table of values and graph.

Let us multiply the y-coordinates of y = √(2x) by 3 to stretch the graph vertically by the factor 3.

When we do as said above, we will get the following table of values and graph.

Let us flip the graph of y = 3√(2x) over the x-axis.

(Because, we have negative sign in front of 3 in the given function)

When we do as said above, we will get the following table of values and graph.

I did both shifts together. I subtracted 4 from each of the x-coordinates and subtracted 1 from each of the y-coordinates of the graph of y = -3√(2x)

When we do as said above, we will get the following table of values and graph.

Translate the graph of y = -3√(2x), 4 units left and 1 unit down in order to get the graph of the given function

y = -3[√(2x+4)] - 1

The graph of the given function y = -3[√(2x+4)] - 1 is given in black color.

After having gone through the stuff given above, we hope that the students would have understood "How to graph functions of the form y = -3[√(2x+4)] - 1 using transformations".

Apart from the stuff given above, if you want to know more about "Using transformations to graph functions of the form y = -3[√(2x+4)] - 1", please click here

Apart from the stuff given in this section, 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**