## About "Stretch a Graph Vertical or Horizontal Examples"

Stretch a Graph Vertical or Horizontal Examples :

Here we are going to learn how to stretch a graph vertically or horizontally.

Stretching a Graph Vertically or Horizontally :

Suppose f is a function and c > 0. Define functions g and h by g(x) = c f(x) and h(x) = f(cx).

Then

• The graph of g is obtained by vertically stretching the graph of f by a factor of c.
• In vertical stretching, the domain will be same but in order to find the range, we have to multiply range of f by the constant "c".
• The graph of h is obtained by horizontally stretching the graph of f by a factor of 1/c.
• In horizontal stretching, the range will be same but in order to find the domain, we have to multiply the domain of f by the constant "1/c".

## Stretching a Graph Vertically or Horizontally - Examples

The procedure for stretching the graph of a function vertically or horizontally is illustrated by the following examples :

Question 1 :

Define a function g by g(x)  =  2f(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 :

(a)  Here the function g(x) is defined by the function f(x), so the domain of both functions will be same. Hence the domain of g in the interval [-1, 1].

(b)  By multiplying each range of f(x) by 2, we get the range of the function g(x).

Range of f(x) by applying domain, we get

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]. By multiplying 2, we get the range of g(x). That is [0, 2].

(c)  Since 2 is the integer multiplied with the function, we have to stretch the graph vertically. Question 2 :

Define a function h by

h(x) = f(2x),

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

(a) Find the domain of h.

(b) Find the range of h.

Solution :

(a)  The formula defining h shows that h(x) is defined precisely when f(2x) is defined, which means that 2x must be in the interval [−1, 1].

Here the constant c is 1/2, which means that x must be in the interval [−1/2 , 1/2 ]. Thus the domain of h is the interval [−1/2 , 1/2].

(b) Because h(x) equals f(2x), 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 [0, 1].  After having gone through the stuff given above, we hope that the students would have understood "Stretch a Graph Vertical or Horizontal Examples".

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