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How is the graph of #y=1/3x^2-4# related to the graph of #f(x)=x^2#?

Answer 1

The lines intersect
#(sqrt(6),6)(-sqrt(6),6)#

The expression for functions is f(x). It is an additional means of displaying the y value since it is dependent upon the variable x. The y value is produced subsequent to the function applying the x value.

Consequently

#f(x) = x^2 # and #y = x^2 # are equivalent.

Since y is the subject of both equations, an inequality can be produced.

#x^2=1/3x^2-4#

Make x the topic of discussion.

#x^2+4=1/3x^2#

#3x^2+12=x^2#

#2x^2 equals -12#

#x^2=-6#

#x=+-sqrt(6)#

After locating the x coordinate, two can be found for the y coordinate. Since there are two values for x, there are two coordinates as well.

#(-sqrt(6),6)#(sqrt(6),6)#

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Answer 2

Eva Abramson

The graph of ( y = \frac{1}{3}x^2 - 4 ) is the graph of ( f(x) = x^2 ) shifted downward by 4 units and compressed vertically by a factor of ( \frac{1}{3} ).

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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.