Problem 1
Domain = {-1, -3, 2, 1}
Range = {5, 0, 2}
The domain is the set of possible inputs and the range is the set of possible outputs. This is a function because each input goes to exactly one output.
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Problem 2
This is a function as well. We do not have any input going to multiple outputs.
Domain = {-2, -3, 5}
Range = {6, 7, 8}
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Problem 3
This is not a function. The input -4 goes to more than one output (outputs 3 and -1 at the same time)
Domain = {-4, -2, 0}
Range = {3, -1, -2, 4}
Answer:
Step-by-step explanation:
(-1,1) and (0,-2) are points on the line
slope of line = (-2-1)/(0-(-1)) = -3
y-intercept = -2
y = -3x - 2
Answer:
The value of the second expression is 12, so the expressions are not equivalent.
Step-by-step explanation:
Answer:
1) 2 and 6 ; 4 and 8 ; 1 and 5 ; 3 and 7
2) 3 and 6 ; 4 and 5
3) 1 and 8 ; 2 and 7
a) Since both limits are <em>distinct</em> and do not exist, we conclude that x = - 1 is not part of the domain of the <em>rational</em> function.
b) The function
is equivalent to the function
.
<h3>How to determine whether a limit exists or not</h3>
According to theory of limits, a function f(x) exists for x = a if and only if
. This criterion is commonly used to prove continuity of functions.
<em>Rational</em> functions are not continuous for all value of x, as there are x-values that make denominator equal to 0. Based on the figure given below, we have the following <em>lateral</em> limits:


Since both limits are <em>distinct</em> and do not exist, we conclude that x = - 1 is not part of the domain of the <em>rational</em> function.
In addition, we can simplify the function by <em>algebra</em> properties:


The function
is equivalent to the function
.
To learn more on lateral limits: brainly.com/question/21783151
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