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How do you use the vertical line test to show #y=3- sqrt(x+2)# is a function?

Answer 1

Eva Abramson

There are no #(x, y_1), (x, y_2)# on the graph#(f)# such that #y_1 \ne y_2#

We want to show that if #(x,y_1) \in \Gamma (f)# and #(x,y_2) \in \Gamma (f)# then #y_1 = y_2#

#y_1 = 3 - sqrt(x + 2)#

#y_2 = 3 - sqrt(x + 2)#

#y_1 - y_2 = 3 - 3 = 0#

#y_1 = y_2#

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Answer 2

Eli Assouline

Apply the vertical line test by drawing vertical lines through the graph. If each vertical line intersects the graph at most once, the function is valid.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.