graph the exponential function.\n\n$f(x)=-\\left(\\frac{5}{2}\\right)^{x}$\n\nplot five points on the graph…

graph the exponential function.\n\n$f(x)=-\\left(\\frac{5}{2}\\right)^{x}$\n\nplot five points on the graph of the function, and also draw the asymptote. then click on the graph - a - function button.

graph the exponential function.\n\n$f(x)=-\\left(\\frac{5}{2}\\right)^{x}$\n\nplot five points on the graph of the function, and also draw the asymptote. then click on the graph - a - function button.

Answer

Explanation:

Step 1: Identify the horizontal asymptote

For exponential functions of the form ( f(x) = -b^x ) where ( b > 1 ), the horizontal asymptote is ( y = 0 ).

Step 2: Calculate points for ( x = -2 )

Substitute ( x = -2 ):
( f(-2) = -\left(\frac{5}{2}\right)^{-2} = -\left(\frac{2}{5}\right)^2 = -\frac{4}{25} = -0.16 )
Point: ( (-2, -0.16) )

Step 3: Calculate points for ( x = -1 )

Substitute ( x = -1 ):
( f(-1) = -\left(\frac{5}{2}\right)^{-1} = -\frac{2}{5} = -0.4 )
Point: ( (-1, -0.4) )

Step 4: Calculate points for ( x = 0 )

Substitute ( x = 0 ):
( f(0) = -\left(\frac{5}{2}\right)^0 = -1 )
Point: ( (0, -1) )

Step 5: Calculate points for ( x = 1 )

Substitute ( x = 1 ):
( f(1) = -\left(\frac{5}{2}\right)^1 = -\frac{5}{2} = -2.5 )
Point: ( (1, -2.5) )

Step 6: Calculate points for ( x = 2 )

Substitute ( x = 2 ):
( f(2) = -\left(\frac{5}{2}\right)^2 = -\frac{25}{4} = -6.25 )
Point: ( (2, -6.25) )

Answer:

Five points: ( (-2, -0.16) ), ( (-1, -0.4) ), ( (0, -1) ), ( (1, -2.5) ), ( (2, -6.25) ); Asymptote: ( y = 0 )