Change to standard form
1 answer:
the equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
distribute and rearrange
y + 1 = 3x - 3 (subtract y from both sides )
1 = 3x - y - 3 ( add 3 to both sides )
3x - y = 4 ← in standard form
the equation of a line in slope-intercept form is
y = mx + c ( m is the slope and c the y-intercept )
rearrange 3x - 2y = 6 into this form
subtract 3x from both sides
- 2y = - 3x + 6 ( divide all terms by - 2 )
y = x - 3 ← in slope-intercept form
y + 2 = - 5x + 5 ( distributing right side )
subtract 2 from both sides
y = - 5x + 3 ← in slope-intercept form
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Answer:
The limit of the function does not exists.
Step-by-step explanation:
From the graph it is noticed that the value of the function is 6 from all values of x which are less than 2. At x=2, the line y=6 has open circle. It means x=2 is not included.
For x<2
The value of the function is -3 from all values of x which are greater than 2. At x=2, the line y=-3 has open circle. It means x=2 is not included.
For x>2
The value of y is 1 at x=2, because of he close circles on (2,1).
For x=2
Therefore the graph represents a piecewise function, which is defined as
The limit of a function exist at a point a if the left hand limit and right hand limit are equal.
The function is broken at x=2, therefore we have to find the left and right hand limit at x=2.
Since the left hand limit and right hand limit are not equal therefore the limit of the function does not exists.