A _____ is a rule that assigns each value of the independent variable to exactly one value of the dependent variable.
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A function is a rule that assigns each vale of the independent variable to exactly one vale of the dependent variable.
The missing word is the function.
Point to remember:
The definition says that two values of x(independent variable ) may correspond to one value of y(dependent variable) but the vice versa is not true( means two values of y(dependent variable ) does not correspond to one value of x(independent variable) ). This explanation is very powerful tool to check that whether a relation is a function or not.
A function is a rule that assigns each value of the independent variable to exactly one value of the dependent variable.
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Find limit as x approaches two from the left of f of x. and limit as x approaches two from the right of f of x..
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The closed point (2,1) is not used to calculate the limit. The closed point (2,1) represents the value of the function at x = 1, but the limit is not the value of the function.
Use the horizontal line that comes from the left and ends at the open point (2,3) to find the limit of f(x) when x approaches to 2 from the left.
That limit is 3, because you can get as close as you want to 3 when you approach x = 2 from the left.
Use the horizontal line that starts at the open point (2-2) and goes to the right, to find the limit of f(x) when x approached to 2 from the right.
That limit is -2 because you can get as close to -2 when you approach x = 2 from the right.
It is important that you know that the definition of limits do not include the value of the function at the point where you want to state the limit.
This result, limit of f(x) when x approaches 2 from the left = 3 and limit of f(x) when x approaches 2 from the right = -2, means that the limit of the function when x approaches 2 does not exist.
The limit exists if and only if the two lateral limits exists and are equal.
A. 12m+4
B. -11m2-3m
C. -11m2+6m
D.5 m + 4
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Answer:
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B.negative one-fourth
C.one-fourth
D.4
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12x+3y=-17
Subtract 12x from both sides:
3y=-12x-17
Divide everything by 3:
y=-4x-17/3
The slope is -4.
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Value = $3,000 [ 1 + 0.05 ] to the 7th power .
Value = $3,000 [ 1.4071 ] = $4,221.30