Find the Range y=tan(x)+2

Problem

y=tan(x)+2

Solution

1. Identify the parent function, which is ƒ(x)=tan(x)

2. Determine the range of the parent function. The tangent function tan(x) takes on all real values as x approaches its vertical asymptotes at x=π/2+n*π

3. State the range of the parent function in interval notation, which is (−∞,∞)

4. Apply the vertical shift. The expression y=tan(x)+2 represents a vertical shift of the graph upward by 2 units.

5. Conclude that adding a constant to a function with a range of all real numbers does not change the range, as ∞+2=∞ and −∞+2=−∞

Final Answer

Range:(−∞,∞)

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