How is the graph of $g (x) = x^{2} + 3$ $g(x)=x^2+3$ related to the graph of $f (x) = x^{2}$ $f(x)=x^2$ ?

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Answer 1 · 2017-01-16T11:24:55

See both graphs in the same frame and compare.

Note that $y_{g} - y_{a} = x^{2} + 3 - x^{2} = 3$ $y_g-y_a = x^2+3-x^2=3$ .

From g to f, it is $(x, y) \to (x, y + 3)$ $(x, y) to (x, y+3)$ .

Also, they are asymptotic to each other.

As $x \to \pm \infty, y_{g} and y_{f} \to \infty$ $x to +-oo, y_g and y_f to oo$ ..

graph{(y-x^2)(y-x^2-3)=0 [-20, 20, -10, 10]}

How is the graph of g(x)=x2+3g(x)=x^2+3 related to the graph of f(x)=x2f(x)=x^2?