Question about Graph of a Function....!Q: Draw the graph of the function:                     Note: Please explain the all steps with Graph

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halcyonsusurrus | Student, Undergraduate | eNotes Newbie

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A function is a map that is well-ordered. Well-ordered is a mathematical concept that means that there is only one possible output value for every input value. An easy way to test this is the Vertical Line Test; the graph is not a function if you can draw a vertical line through any two points of the graph.

Consider the graph of $y = x^2$ and $y = \sqrt{x}$. [The dollar signs show LaTeX notation.] You can even put "x^2, sqrt(x)" into the google search bar to see these two graphs together.

Do you see how both -2 and 2 produce the value 4 in the graph for $y = x^2." The square root function is the inverse function of $y = x^2$. (Even if you didn't already know that, you can see it is true either by solving for it or by seeing that the square root function is the $y = x^2$ function reflected over the line $y = x$.) Do you see how a part of the square root function is "missing?" This is to allow the square root function to satisfy the Vertical Line Test.

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