What is the increasing/decreasing interval, max/min, rate of change etc of these functions?

Question

Hi, can someone please help me with this : 

 

For f(x)=-2x+3 , what is the type of variation, rate of change, increasing and decreasing interval , where is it positive and negative, and what is the maximum and minimum ? 

 

For f(x)= x , what is the type of variation, rate of change, increasing and decreasing interval , where is it positive and negative, and what is the maximum and minimum ? 

 

For f(x) = 3 , what is the type of variation, rate of change, increasing and decreasing interval , where is it positive and negative, and what is the maximum and minimum ? 

Answer 1

For.f(x) = 2x + 3  this is linear variation (The graph of this equation is a straight line with slope = 2 and y-intercept =3.

It's rate of change is its slope or 2.

It is increasing for x>0 and decreasing for x<0

It is positive for x> -3/2 and negative for x <-3/2

It has no maximum or minimum  It ranges from -infinity

to + infinity

 

For f(x) = x  Also a linear equation whose slope is 1 and y-intercept is 0.  Its rate of change is 1.  It increases for x>0 and dcreases for x<0  It is positive for x>0 and negative for x<0  It also has no minimm or maximum

 

f(x) =3 is constant variation.  It's graph is a horizontal straight line.  It's rate of variation is 0.  There is no increasing or decreasing interval.  It is positive for all x and negative for no value of x.  The maximum and minimum value is 3.