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How are the graphs #f(x)=x^3# and #g(x)=(x+2)^3-5# related?

Answer 1

The function #f(x) = x^3 # is the parent function of #g(x)#.
The graph below is #g(x)#.
graph{(x+2)^3 -5 [-8, 8, -15, 15]}

The function #f(x)# would have the curve positioned at the origin. The function #g(x) # has been shifted horizontally to the left by #2# and shifted vertically down by #5#.

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Answer 2

Caleb Alexander

The graphs of ( f(x) = x^3 ) and ( g(x) = (x + 2)^3 - 5 ) are related by a horizontal shift and a vertical shift.

( g(x) = (x + 2)^3 - 5 ) represents the function ( f(x) = x^3 ) shifted 2 units to the left and 5 units downward. This means the graph of ( g(x) ) will be identical to the graph of ( f(x) ), but shifted 2 units to the left along the x-axis and 5 units downward along 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.