Question

Graph comparison:
In the image (at the end, below) you can find the function $f (x) = 3^{x}$ and $g(x) = log_{3} x$

a) Which curve represents the graph of the function f (x)? And g (x)?

b) What is the relationship between f (x) and g (x)?

Answer 1

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Answer:

  a) left curve: f(x); right curve: g(x)

  b) the functions are inverses of each other

Step-by-step explanation:

(a) An exponential function with a base greater than 1 has increasing slope. A log function has decreasing slope. The exponential function is on the left.

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(b) The base of the exponential is the same as the base of the logarithm, so these functions are inverses of each other. This can be seen in the fact that each is a reflection of the other in the line y=x.