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Using the graph of #f(x)=x^2# as a guide, describe the transformations, and then graph the function #g(x)=-2x^2#?

Answer 1

#f(x)=x^2# #(x,y)# graph{x^2 [-15, 15, -20, 20]}

#h(x)=color(red)(2)x^2# Stretch by a vertical factor of #2#. (The graph rises faster and becomes skinnier.) #(x,2y)# graph{2x^2 [-15, 15, -20, 20]}

#g(x)=color(red)(-)2x^2# Reflect the function across the #x#-axis. #(x,-2y)# graph{-2x^2 [-15, 15, -20, 20]}

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Answer 2

Sadie Allen

The function g(x) = -2x^2 is obtained by applying the following transformations to the function f(x) = x^2:

Vertical compression by a factor of 2.
Reflection across the x-axis.

The graph of g(x) = -2x^2 will be narrower than the graph of f(x) = x^2, and it will open downwards due to the negative coefficient of x^2.

To graph g(x) = -2x^2, start with the graph of f(x) = x^2, then vertically compress it by a factor of 2, and finally, reflect it across the x-axis.

The resulting graph will be a downward-opening parabola that is narrower than the graph of f(x) = x^2.

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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.