In 2003, the population of a certain country per square mile of land area was 87. In 2000, the person per square mile population was 84.6. Assume the relationship between years and persons per square mile is a linear relationship.
a. Write an equation, in slope-intercept form, describing the relationship between year and persons per square mile. Use ordered pairs of the form (x, y), where x is the
number of years past 2000 and y is persons per square mile.
b. Use this equation to predict the person per square mile population in 2020,

(x, y)→(x − 8, y − 7)

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let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

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