What is the range?

Question

What is the range of these equations?

 

y = 2x + 3, x<1

y = -x, x≥1

 

I've graphed the two equations, but I'm not sure how to find the range.

 

Thank you for your help!

Answer 1

The range is the set of all possible output values of y

 

1.  y = 2x + 3, x<1

 

The slope is positive... m= 2... so this is an increasing function

The highest range value would be at y=5 when x=1

but it never actually reaches 5 since x<1

Range (-∞, 5)

 

2.  y = -x, x≥1

 

This has a negative slope so this is a decreasing function

The highest value of the range is y=-1 at x=1

Range (-∞, -1]

Answer 2

As you probably know, the range would be all the y values (or f(x) values).  It looks like the combined range for these functions is -inf to +5.