How do you graph the function #f(x)=3# and its inverse?
graph{y=3+0.000001x [-10, 10, -5, 5]}
graph{x=3+0.00001y [-10, 10, -5, 5]}
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To graph the function ( f(x) = 3 ) and its inverse, follow these steps:
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For the function ( f(x) = 3 ), note that it is a horizontal line passing through the point ( (x, y) = (0, 3) ).
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To find the inverse function, swap the roles of ( x ) and ( y ) in the equation. The inverse function is ( f^{-1}(x) = y = 3 ).
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The inverse function ( f^{-1}(x) = 3 ) is also a horizontal line passing through ( (x, y) = (3, 0) ).
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Plot these points on the Cartesian plane and draw the horizontal lines representing the functions ( f(x) = 3 ) and its inverse ( f^{-1}(x) = 3 ).
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The graph of ( f(x) = 3 ) is a horizontal line parallel to the x-axis, passing through ( y = 3 ).
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The graph of its inverse ( f^{-1}(x) = 3 ) is also a horizontal line parallel to the x-axis, passing through ( x = 3 ).
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These two lines are reflections of each other across the line ( y = x ) because the inverse function undoes the action of the original function.
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Thus, the graph of ( f(x) = 3 ) and its inverse ( f^{-1}(x) = 3 ) are both horizontal lines.
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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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