To determine if the relationship represented by an equation is a function, you need to check if each input (x-value) corresponds to a unique output (y-value). Here are a few ways to determine if an equation represents a function:
1. Vertical Line Test: Plot the points that satisfy the equation and draw vertical lines through them. If any vertical line intersects the graph at more than one point, then the equation does not represent a function.
2. Algebraic Approach: Solve the equation for y in terms of x. If for every valid input x, there is exactly one output y, then the equation represents a function. If there are multiple y-values for a single x-value, then the equation does not represent a function.
3. Table of Values: Create a table listing various x-values and evaluate the equation to find the corresponding y-values. If there are no repeated values in the y-column, then the equation represents a function. If there are repeated y-values for a single x-value, then the equation does not represent a function.
Remember that for a relationship to be considered a function, every input should have exactly one output.
How can you tell from an equation is the relationship is a function?
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