graph the exponential function ( g(x)=3^{x - 2} ).\nto do this, plot two points on the graph of the…

graph the exponential function ( g(x)=3^{x - 2} ).\nto do this, plot two points on the graph of the function, and also draw the asymptote. then click on the graph - a - function button.\nadditionally, give the domain and range of the function using interval notation.\ndomain:\nrange:

graph the exponential function ( g(x)=3^{x - 2} ).\nto do this, plot two points on the graph of the function, and also draw the asymptote. then click on the graph - a - function button.\nadditionally, give the domain and range of the function using interval notation.\ndomain:\nrange:

Answer

Explanation:

Step 1: Identify the horizontal asymptote

For exponential functions ( a^{x-h} ), the horizontal asymptote is ( y = 0 ).

Step 2: Calculate two points on the graph

  • When ( x = 2 ): ( g(2) = 3^{2-2} = 3^0 = 1 ) → Point: ( (2, 1) )
  • When ( x = 3 ): ( g(3) = 3^{3-2} = 3^1 = 3 ) → Point: ( (3, 3) )

Step 3: Determine the domain

All exponential functions have a domain of all real numbers.

Step 4: Determine the range

Since ( 3^{x-2} > 0 ) for all ( x ), the range is all positive real numbers.

Answer:

Domain: ( (-\infty, \infty) )
Range: ( (0, \infty) )