Graph of f(x-3) is compressed by a factor of horizontally of f(x).
<u>Step-by-step explanation:</u>
We have, the graph of f(x)= , on replacing f(x) by f(x-3) we get:
=
.Below shown are the images for graph of f(x) and f(x-3). Both are functions are exponential , and so having exponential graph but f(x-3) is compressed by a factor of
horizontally . Domain and range of both functions are same i.e. F(x) & f(x-3) domain & range are same , just difference in graph :
.
Answer:
a)
b)
c)
d)
Step-by-step explanation:
a)
When factoring a binomial (a polynomial with two terms), what we will be looking for are the terms that are shared between them.
In this problem, it can be seen that both of these terms have and x. This means that we can factor it out to get
b)
What are the common terms here?
It can be seen that each of these share a 2x, so our factored form would be
c)
What about this one?
The common factor of this one is 5x, so our factored form would be
d)
The common factor of this one is , so our factored form would be
The ratio of the area of region R to the area of region S is:
The sides of R are in the ratio : 2:3
Let the length of R be: 2x
and the width of R be: 3x
i.e. The perimeter of R is given by:
( Since, the perimeter of a rectangle with length L and breadth or width B is given by:
)
Hence, we get:
i.e.
Also, let " s " denote the side of the square region.
We know that the perimeter of a square with side " s " is given by:
Now, it is given that:
The perimeters of square region S and rectangular region R are equal.
i.e.
Now, we know that the area of a square is given by:
and
Hence, we get:
and
i.e.
Hence,
Ratio of the area of region R to the area of region S is: