Describe the graphs of the functions f(x) = 2x - 1 and g(x) = -2x - 1. Compare and contrast the domain and range of f(x) and g(x).

Question

Describe the graphs of the functions f(x) = 2x - 1 and g(x) = -2x - 1. Compare and contrast the domain and range of f(x) and g(x).

Answer 1

f(x) is a straight line with a slope of 2 and a y-intercept of -1.  The x-intercept is 1/2.  

g(x) is a straight line with a slope of -2 and a y-intercept of -1.  The x-intercept is -1/2.  

For linear functions the domain and range are always all real numbers so f(x) and g(x) have the same domain and range.  

 

Answer 2

f(x)=2x-1 and g(x)=-2x-1.

 

The reflection of f(x) over y-axis is f(-x) and f(-x)=-2x-1=g(x)

 

This tells us that g(x) is a reflection of f(x) over y-axis.  

 

Both functions f and g return real numbers for all values of x.  Therefore the domain for both functions is (-∞,∞).  Both functions are straight lines and have a range of (-∞,∞).