How is the graph of #h(x)=1.01x^2-6.5# related to the graph of #f(x)=x^2#?

Answer 1

The base function is the same (i.e. #x^2#).

Both f(x) and h(x) have the same base function; the only differences are that h(x) does not have the same vertex or opening, but they are related because they are both parabolic functions (#x^2#).

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Answer 2

Kennedy Adams

Its is scaled in the #x#-direction by a factor of #1.01#.

Its is translated down in the #y#-direction by #6.5# units.

The following translations relate the graphs of the functions #y=h(x)# to the function #y=f(x)##:

The following are the graphs:

# y = f(x) = x^2#

x^2 [-10, 10, -8, 8]} graph

#x = 1.01x^2-6.5 #y = h(x) #

chart{1.01x^2-6.5 [-10, 10, -8, 8]}

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Answer 3

Eli Assouline

The graph of h(x) = 1.01x^2 - 6.5 is related to the graph of f(x) = x^2 by stretching the graph vertically by a factor of 1.01 and shifting it downward by 6.5 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.