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From the statement, A and B are correct.

The two given graphs f(x) and g(x) are exponential functions graph. Exponential function doesn’t have a vertical asymptote. Also the horizontal asymptote is one.  

Further Explanation

One of the important functions in mathematics is the exponential function. Although, linear functions ranks higher than exponential. For exponential functions to be formed, the independent variable will have to be exponent. Exponential function are basically the solutions to dynamics systems, particular the simplest types.  

Exponential functions are commons and they involve exponents. The differences they have with other functions is that the variable is the power instead of the base.

Exponential functions have positive number other than 1

Vertical Asymptote refers to vertical line which corresponds to zeros of the denominator of rational function. They can come up in any context such as logarithms, but are mostly present in the context of rationals. It is also a line that the functions of a graph approaches but don’t touches. Rational functions have asymptote.  

Horizontal Asymptote refers to horizontal line that shows the behavior of function at the edges of a graph. It is basically not a sacred ground, although the function can cross over or touch the asymptote.

KEYWORDS:

  • vertical asymptote
  • horizontal asymtote
  • exponential function
  • base
  • graph

Option A is correct and Option B is correct.

Further explanation:

Given:

The options are as follows,

A. Both graphs have exactly one asymptote.

B. Both graphs are exponential function.

C. Both graphs are logarithmic functions.

D. Both graphs have been shifted and flipped.

Explanation:

A line or a curve that approaches to zero as point approaches to infinity.

The vertical asymptote is point at which the function is not defined.

Exponential function are those function which can be written in the form of [tex]y = c{d^x}.[/tex]

Initially the value of exponential function increases slowly but increases faster later on.

The functions are [tex]f\left( x \right)[/tex] and [tex]g\left( x \right).[/tex]

From the graph it has been observed that the functions grow exponentially. Therefore, the functions are exponential.

It also been observed that the functions have only one asymptote.

Option A is correct.

Option B is correct.

Option C is not correct.

Option D is not correct.

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function https://brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Functions

Keywords: asymptote, both graph, exactly one asymptote, exponential function, logarithmic function, shifted, flipped, functions, statements, true.