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Which quadrants and axes does #f(x)=x-sqrt(x+5)# pass through?

Answer 1

#I#, #III# and #IV# quadrants and it passes through y-axis at #(0,-sqrt(5))# and x-axis at #(sqrt(21)/2+1/2,0)#.

graph{x-sqrt(x+5) [-6.407, 7.64, -5.67, 1.356]}

As you can see the graph passes through #I#, #III# and #IV# quadrants.

To know the y-axis point you have to substitute de #x# by #0#. So: #f(x)=x-sqrt(x+5) ➝ f(0)=0-sqrt(0+5)=-sqrt(5)≈-2.236# And you get the point #(0,-sqrt(5))#.

To know the x-axis point(s) you have to equal the function to #0#. So: #f(x)=x-sqrt(x+5)=0# you isolate the variable #x#: #x=sqrt(21)/2+1/2≈2.79# So you get the point #(sqrt(21)/2+1/2,0)#.

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Answer 2

Kennedy Adams

The function ( f(x) = x - \sqrt{x + 5} ) passes through quadrants I and II and intersects both the x-axis and the y-axis.

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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.