A linear function is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable. For example, a common equation,
y
=
m
x
+
b
, (namely the slope-intercept form, which we will learn more about later) is a linear function because it meets both criteria with
x
and
y
as variables and
m
and
b
as constants. It is linear: the exponent of the
x
term is a one (first power), and it follows the definition of a function: for each input (
x
) there is exactly one output (
y
). Also, its graph is a straight line.
Answer:
-- Proved

Step-by-step explanation:
Given


Required
Show that 
The volume is calculated as:

Open the brackets



Collect Like Terms


Divide through by 4


Solving further:
Expand the expression

Factorize:


Split:


(x,y)
x=input
y=output
example
we see
g=(1,2)
theefor
g(1)=2
a.
f(4)=1
g(1)=2
g(f(4))=2
b.
g(-2)=4
f(4)=1
f(g(-2))=1
c.
f(3)=5
g(5)=5
f(5)=0
f(g(f(3)))=0
Answer: The consultant earn $50 each hour.
Explanation:
It is given that for 4 hours of work, the consultant charges $400. For 5 hours of work, she charges $450. The amount that a consultant charges for her work can be modeled using a linear function.
If the linear function represents the amount earn by consultant in hours the the coordinates can be written as (4, 400) and (5, 450).
If we want to find how much money does the consultant earn each hour, so first we have to find the slope of linear function which passing through two points (4, 400) and (5, 450).




In the linear function the slope show the earning of consultant per hour, therefore consultant earn $50 each hour.