Problem

Compare the domain and range of each function: \(y=x^2\) over all real \(x\) and \(y=2x+1\) over all real \(x\).

Actual source graphs distinguishing the continuous and discrete functions or the stated function families.

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Both functions have domain all real numbers because the question says “over all real x”; for y=x² the range is y≥0, and for y=2x+1 the range is y≥1 because the +1 shifts the graph up.

Both functions have domain all real numbers because the question says “over all real x”; for y=x² the range is y≥0 since squares are never negative, and for y=2x+1 the range is all real numbers because a nonhorizontal line can output any real value.

Both functions have domain all real numbers because the question says “over all real x”; the range of y=x² is also all real numbers since x can be any real number, and the range of y=2x+1 is all real numbers.

For both functions, the domain is y≥0 because outputs cannot be negative, while the range is all real numbers since x can be any real number in each equation.

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Compare the domain and range of each function: \(y=x^2\) over all real \(x\) and \(y=2x+1\) over all real \(x\).

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