Solve the system of equations: y= 3x y= x^2 - 4
1 answer:
Answer:
Step-by-step explanation:
Make both equations equal to each other and solve for the variable x:
Find two numbers that when you add them you get -3 and the product of both numbers be -4. These numbers are 1 and -4. Then:
Substitute these values into one the original equations and solve for y:
Therefore, you get that:
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A relation is any set of ordered pairs, which can be thought of as (input, output).
A function is a relation in which NO two ordered pairs have the same first component and different second components.
The set of first components (x-coordinates) in the ordered pairs is the DOMAIN of the relation.
The set of second components (y-coordinates) is the RANGE of the relation.
Part 1:
Domain: {-1, 1, 3, 6}
Range: {2, 2, 2, 2}
Part 2:
To determine whether the given relation represents a function, look at the given relation and ask yourself, “Does every first element (or input) correspond with EXACTLY ONE second element (or output)?”
Remember that a function can only take on 1 output for each input.
It helps to plot the points on the graph and perform the Vertical Line Test (VLT):
The Vertical Line Test allows us to know whether or not a graph is actually a function. If a vertical line intersects the graph in all places at exactly one point, then the relation is a function.
As you can see in the attached screenshot, every vertical line drawn only has 1 point in it. This means that each x-value corresponds to exactly one y-value. The given relation passed the VLT. Therefore, the relation is a function.
Please mark my answers as the Brainliest if you find my explanation helpful :)
A function is a relation in which NO two ordered pairs have the same first component and different second components.
The set of first components (x-coordinates) in the ordered pairs is the DOMAIN of the relation.
The set of second components (y-coordinates) is the RANGE of the relation.
Part 1:
Domain: {-1, 1, 3, 6}
Range: {2, 2, 2, 2}
Part 2:
To determine whether the given relation represents a function, look at the given relation and ask yourself, “Does every first element (or input) correspond with EXACTLY ONE second element (or output)?”
Remember that a function can only take on 1 output for each input.
It helps to plot the points on the graph and perform the Vertical Line Test (VLT):
The Vertical Line Test allows us to know whether or not a graph is actually a function. If a vertical line intersects the graph in all places at exactly one point, then the relation is a function.
As you can see in the attached screenshot, every vertical line drawn only has 1 point in it. This means that each x-value corresponds to exactly one y-value. The given relation passed the VLT. Therefore, the relation is a function.
Please mark my answers as the Brainliest if you find my explanation helpful :)