Domain and range are not sufficient to determine the y intercept.
For example, the domain and range for the straight line y = 2x + 3 are the whole of the real numbers. That tells you nothing about the intercept.
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The domain and range are the x and y coordinates of the dot, respectively.
You need to know the domain in order to find the range.
The domain is a subset of the values for which the function is defined. The range is the set of values that the function takes as the argument of the function takes all the values in the domain.
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The domain consists of all values of x for which there is a point on the graph. Similarly, the range applies to all the y values.