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Given #f(x)=x^2 - 7#, how do you describe the transformation?

Answer 1

the graph of function f is downward shift of 3 units.

suppose that #y=g(x)# one of the coordinates include (a,b)

then if #y=g(x)+c# then the coordinates becomes (a,b+c)

when c>0 the graph is upward shift of c unit when c<0 the graph is downward shift of c unit. the transformation of here is a vertical translation.

note that #f(x)# is a quadratic function. so when #f(x)=x^2# the graph should look like this graph{x^2 [-10, 10, -5, 5]}

so now since #f(x)=x^2-3# so the graph look like this. graph{x^2-3 [-10, 10, -5, 5]}

the graph of function f is downward shift of 3 units.

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Answer 2

Serenity Johnson

The function ( f(x) = x^2 - 7 ) is a quadratic function. It represents a transformation of the parent function ( f(x) = x^2 ) where each ( x ) value is squared and then subtracted by 7. This transformation shifts the graph of the parent function downward by 7 units. Therefore, the transformation can be described as a vertical translation downward by 7 units.

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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.