Is the relation {(3,−2), (−2,3), (−2,4) (4,3)}
a function?
Yes, the relation {(3,-2), (-2,3), (-2,4), (4,3)} is a function. To be a function, each input ("x-value") must have exactly one corresponding output ("y-value"). In this relation, each x-value occurs only once, and there are no duplicate x-values with different y-values. Therefore, it satisfies the criteria to be a function.
What is the domain of the relation: {(3,−2), (−2,3), (−2,4) (4,3)}
?
The domain of a relation refers to all the possible input values, or x-values. In this relation, the x-values are 3, -2, and 4. Therefore, the domain of this relation is {3, -2, 4}.
What is the range of the relation: {(3,−2), (−2,3), (−2,4) (4,3)}
?
The range of a relation refers to all the possible output values, or y-values. In this relation, the y-values are -2, 3, and 4. Therefore, the range of this relation is {-2, 3, 4}.
Determine if y=2(x−3)^2 +6
a function by graphing. (Hint: you can use desmos or geogebra).
To determine if the equation y = 2(x-3)^2 + 6 is a function, we can graph it and check if there are any points where a vertical line intersects the graph at more than one point.
Here is a link to the graph of the equation on Desmos: https://www.desmos.com/calculator/1zks6veawx
Upon graphing the equation, it is clear that every vertical line intersects the graph at most once. Therefore, the equation y = 2(x-3)^2 + 6 represents a function.
Determine if x^2+y^2=9
is a function by graphing.
To determine if the equation x^2 + y^2 = 9 is a function, we can graph it and check if there are any points where a vertical line intersects the graph at more than one point.
Here is a link to the graph of the equation on Desmos: https://www.desmos.com/calculator/srhzckndkn
Upon graphing the equation, we can observe that it is a circle centered at the origin with a radius of 3. Since the circle passes through points in multiple places for a single x-value, the equation x^2 + y^2 = 9 does not represent a function.