Question

Find the domain.

f(x)= 3 - 1/2x if x less than or equal to 2

= 2x - 5 if x > 2


Please help... an explanation would be wonderful, so I can understand how to do this.

Answer 1

Your graph is made up of two separate straight lines, that change at x = 2
for all values of x ≤ 2 you have the straight line
y = (-1/2)x - 3 , with slope -1/2 and y-intercept of -3
(draw the line through (0,-3) and (-6,0) as a ray starting at (2,-4)

for x > 2 you have the line y = 2x - 5 , slope = 2 and y-intercept of -5
(draw line from (2,-1) and (5,5) as a ray starting at (2,-1) but draw an empty circle around (2,-1) to show that this point is excluded.

Since any x can be used in the appropriate equation, the domain is the set of real numbers.

Answer 2

Thank you very much for explaining.