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Which of the following statements are true?

A. both graphs have been shifted and flipped

B. Both graphs are logarithmic functions

C. Both graphs are exponential functions.

D. Both graphs have exactly one asymptote

Which of the following statements are true A both graphs have been shifted and flipped B Both graphs are logarithmic functions C Both graphs are exponential fun class=

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Answer:

Option: D  Both graphs have exactly one asymptote.

Step-by-step explanation:

  • Clearly by looking at the graph of the two functions i.e. f(x) and g(x) we could observe that the graph of function f(x) is similar to the graph of the exponential function and the graph of the function g(x) is similar to the graph of the logarithmic function.

Hence, Option: B and option: C are discarded.

  • Also we could observe that the graph of the function f(x) with respect to the parent function [tex]e^x[/tex] is shifted by some units above but not flipped.
  • The graph of the function g(x) with respect to the parent function log (x) is both shifted as well as flipped.

Hence, option: A is discarded.

  • Also, we know that both the exponential function and the logarithmic function have exactly one asymptote.

Hence, option: D is the correct answer.

 

A function assigns the values. The correct option is D.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

For the two of the given functions, it is easily observed that the function g(x) is not a transformed function of f(x) or vice versa. Thus, option A is incorrect.

Since the function f(x) is an exponential function and g(x) is a logarithmic function, therefore, options B and C are incorrect.

For the two of the given function, it can be observed that both the functions will have an asymptote. Hence, the correct option is D.

Learn more about Function:

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