## About "Reflecting a Graph in the Horizontal or Vertical Axis"

Reflecting a Graph in the Horizontal or Vertical Axis :

Here we are going to learn how to reflect the graph in the horizontal and vertical axis.

How to find the graph of reflection of the horizontal or vertical axis :

Suppose f is a function. Define functions g and h by

g(x) = −f(x) and h(x) = f(−x).

Then

• The graph of g is the reflection of the graph of f through the horizontal axis;
• The graph of h is the reflection of the graph of f through the vertical axis.

Important Note :

The domain of g is the same as the domain of f, but the domain of h is obtained by multiplying each number in  the domain of f by −1.

## Reflecting a Graph in the Horizontal or Vertical Axis - Examples

The procedure for reflecting the graph of a function through the horizontal axis is illustrated by the following examples:

Question 1 :

Define a function g by

g(x) = −f(x)

where f is the function defined by f(x) = x2, with the domain of f the interval [−1, 1].

(a) Find the domain of g.

(b) Find the range of g.

(c) Sketch the graph of g.

Solution :

From the given question g(x)  =  - f(x), we come to know that, we have to perform horizontal reflection.

(a)  According to the definition domain of both functions will be same. So the domain of g(x) is [-1, 1]

(b)  To find the range of g, let us find the range of f(x) using the domain [-1, 1].

f(x) = x2

If x = -1, then y = 1

If x = 0, then y = 0

If x =-1, then y = 1

Range of f(x) is [0, 1]. The range of g(x) can be obtained by multiply -1 with the range of f(x). Hence the range of g(x) is [-1, 0].

(c)  Sketching the graph :

Question 2 :

Define a function h by h(x) = f(−x),

where f is the function defined by f(x) = x2, with the domain of f the interval [1/2 , 1].

(a) Find the domain of h.

(b) Find the range of h.

(c) Sketch the graph of h.

Solution :

From the given question h(x)  =  f(-x), we come to know that, we have to perform reflection of y axis.

(a)  According to the definition,to get the domain of the function g(x), we have to multiply the domain of f(x) by the coefficient of 1, that is -1.

So the domain of g(x) is [-1, -1/2]

(b) Because h(x) equals f(−x), we see that the values taken on by h are the same as the values taken on by f . Thus the range of h equals the range of f , which is the interval [ 1/4 , 1].

(c)  Sketching the graph :

After having gone through the stuff given above, we hope that the students would have understood "Reflecting a Graph in the Horizontal or Vertical Axis".

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

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

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

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

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

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

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

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

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