introduction to exponential functions\naccording to the mini - lesson, which of the following are true…

introduction to exponential functions\naccording to the mini - lesson, which of the following are true regarding ( f(x)=a(b)^{x} )? check all that apply. assume ( a>0 ).\nthe domain of the exponential functions is ( x>0 ).\nthe range of the exponential functions is ( f(x)>0 ).\nthe horizontal asymptote is the line ( y = 0 ).\nthe horizontal asymptote is the point ( (0,a) ).\nthe horizontal asymptote is the line ( x = 0 ).\nthe domain of the exponential functions is all real numbers.\nthe range of the exponential functions is all real numbers.

introduction to exponential functions\naccording to the mini - lesson, which of the following are true regarding ( f(x)=a(b)^{x} )? check all that apply. assume ( a>0 ).\nthe domain of the exponential functions is ( x>0 ).\nthe range of the exponential functions is ( f(x)>0 ).\nthe horizontal asymptote is the line ( y = 0 ).\nthe horizontal asymptote is the point ( (0,a) ).\nthe horizontal asymptote is the line ( x = 0 ).\nthe domain of the exponential functions is all real numbers.\nthe range of the exponential functions is all real numbers.

Answer

Brief Explanations:

  • Domain: For an exponential function (y = a(b)^{x}) ((a>0)), (x) can be any real number. So the domain is all real numbers, not (x > 0).
  • Range: Since (a>0) and (b^{x}>0) for (b>0,b\neq1), then (y=a(b)^{x}>0). The range is (y>0), not all real numbers.
  • Horizontal Asymptote: As (x\rightarrow-\infty) (if (b > 1)) or (x\rightarrow\infty) (if (0 < b<1)), (y=a(b)^{x}\rightarrow0). The horizontal asymptote is (y = 0). A horizontal asymptote is a line (not a point), and (x = 0) is a vertical line (not a horizontal asymptote).

Answer:

  • The Range of the exponential functions is (f(x)>0).
  • The Horizontal Asymptote is the line (y = 0).
  • The Domain of the exponential functions is All Real Numbers.