Which values of x are point(s) of discontinuity for this function? Please explain how you did it.
2 answers:
<span>The correct answers are:
x = 0
x = 2
Explanation:
When x < 0, the value of y = -</span>
<span>.
When x > 0, the value of y = </span><span>.
When x = 0, there is no value of y mentioned in the conditions; it means that there is discontinuity at x = 0.
When x < 2, the value of y = </span><span>.
When x >= 2, the value of y = 2.
It means that, at x = 2, there is a discontinuity because the graph of y = </span> is not touching the graph of y = 2 at x = 2.
x = 0
x = 2
Explanation:
When x < 0, the value of y = -</span>
When x > 0, the value of y = </span>
When x = 0, there is no value of y mentioned in the conditions; it means that there is discontinuity at x = 0.
When x < 2, the value of y = </span>
When x >= 2, the value of y = 2.
It means that, at x = 2, there is a discontinuity because the graph of y = </span>
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The line y = mx + c has a slope of m.
Parallel line:
A parallel line will also have a slope of m, and should be of the form
y = mx + k
Because the line passes through the point (a,b), therefore
ma + k = b
k = b - ma
The equation of a parallel line is
y = mx + b - ma
= m(x-a) + b
Perpendicular line:
A perpendicular line will have a slope of -1/m, because the product of slopes should be -1.
The equation for a perpendicular line is of the form
y = -(1/m)x + k
Because the line passes through (a,b), therefore
-(1/m)a + k = b
k = b + a/m
The equation for a perpendicular line is
y = -(x/m) + b + a/m
= -(1/m)(x-a) + b
Answer:
Parallel line:
Perpendicular line:
Parallel line:
A parallel line will also have a slope of m, and should be of the form
y = mx + k
Because the line passes through the point (a,b), therefore
ma + k = b
k = b - ma
The equation of a parallel line is
y = mx + b - ma
= m(x-a) + b
Perpendicular line:
A perpendicular line will have a slope of -1/m, because the product of slopes should be -1.
The equation for a perpendicular line is of the form
y = -(1/m)x + k
Because the line passes through (a,b), therefore
-(1/m)a + k = b
k = b + a/m
The equation for a perpendicular line is
y = -(x/m) + b + a/m
= -(1/m)(x-a) + b
Answer:
Parallel line:
Perpendicular line: