How do you sketch the graph #g(x)=-x^5-3# and #f(x)=x^5# using transformations and state the domain and range of g?

Answer 1

#g(x) = -f(x) - 3# Domain and range = #RR#

If you know x^5 is like x^3 but is not like x^1 because it's not a straight line, then

#f(x) = x^5# Domain and range = #RR# #(x,y) mapsto (x,-y)# Reflection on 0y axis. #(x, -y) mapsto (x, -y - 3)# Vertical translaction #y := y - 3#
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Answer 2

To sketch the graph of ( g(x) = -x^5 - 3 ) using transformations relative to the graph of ( f(x) = x^5 ), and to state the domain and range of ( g(x) ), follow these steps:

  1. Graph Transformations:

    • Reflection over the x-axis: The negative sign in front of ( x^5 ) reflects the graph of ( f(x) = x^5 ) over the x-axis.
    • Vertical shift down: The "-3" term shifts the graph vertically downward by 3 units.
  2. Sketching the Graph: Start with the graph of ( f(x) = x^5 ) and apply the transformations:

    • Reflect the graph over the x-axis.
    • Shift the resulting graph downward by 3 units.
  3. Domain and Range:

    • Domain: The domain of ( g(x) ) is all real numbers, as there are no restrictions on the input values of ( x ).
    • Range: Since the graph of ( g(x) ) is a reflection of the graph of ( f(x) = x^5 ) over the x-axis and shifted downward by 3 units, the range of ( g(x) ) is all real numbers.
  4. Sketching the Graph of ( g(x) ): Start with the graph of ( f(x) = x^5 ), reflect it over the x-axis, and then shift it downward by 3 units.

  5. State the Domain and Range of ( g(x) ):

    • Domain: ( (-\infty, \infty) ) (all real numbers)
    • Range: ( (-\infty, \infty) ) (all real numbers)
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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.

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.

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.

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.

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