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.
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.
Thank you very much for explaining.
To find the domain of a function, we need to determine the set of all possible values that x can take. In this case, we have a piecewise defined function, meaning the function has different rules depending on the value of x.
Let's consider the first rule: f(x) = 3 - 1/2x if x is less than or equal to 2. In this case, x can take any value less than or equal to 2. So, the domain for this part of the function would be x ≤ 2.
Now, let's consider the second rule: f(x) = 2x - 5 if x is greater than 2. In this case, x can take any value greater than 2. So, the domain for this part of the function would be x > 2.
To find the domain of the entire function, we need to combine the domains from both parts. Since x can be either less than or equal to 2 or greater than 2, the domain of the function can be expressed as:
Domain: x ≤ 2 or x > 2