How do you graph the function #f(x)=3# and its inverse?

Answer 1

#f(x)=3# has a graph which is a horizontal line. The inverse relation (not a function) has a graph which is a vertical line.

The graph of #f(x) = 3# is a horizontal line #y=3# through #(0, 3)#...

graph{y=3+0.000001x [-10, 10, -5, 5]}

To obtain the graph of the inverse, we can reflect this graph in the diagonal line #y=x# to get:

graph{x=3+0.00001y [-10, 10, -5, 5]}

If that does not look like the graph of a function to you, that's probably because it isn't. The only value of #x# for which there are any values of #y# is #x=3# and then there are an infinite number of values to choose from.
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Answer 2

To graph the function ( f(x) = 3 ) and its inverse, follow these steps:

  1. For the function ( f(x) = 3 ), note that it is a horizontal line passing through the point ( (x, y) = (0, 3) ).

  2. To find the inverse function, swap the roles of ( x ) and ( y ) in the equation. The inverse function is ( f^{-1}(x) = y = 3 ).

  3. The inverse function ( f^{-1}(x) = 3 ) is also a horizontal line passing through ( (x, y) = (3, 0) ).

  4. 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 ).

  5. The graph of ( f(x) = 3 ) is a horizontal line parallel to the x-axis, passing through ( y = 3 ).

  6. The graph of its inverse ( f^{-1}(x) = 3 ) is also a horizontal line parallel to the x-axis, passing through ( x = 3 ).

  7. These two lines are reflections of each other across the line ( y = x ) because the inverse function undoes the action of the original function.

  8. Thus, the graph of ( f(x) = 3 ) and its inverse ( f^{-1}(x) = 3 ) are both horizontal lines.

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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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