The correct answer is:
[A]: "
Graph A"
{the red graph
}.
______________________________________________________Note: _______________________________When x = 0 ;
y = f(x) = 5(2)⁻ˣ = 5* (2)⁻⁰ = 5 * 1 = 5 .
_______________________________By inspection of the graph, the only given answer choices with graphs that fall on the point "(0, 5)" are:
[A]: "Graph A" (the red graph) ; and:
[B]: "Graph B" (the green graph) .
________________________________________________________Now, let us look at other points and see if the selected points are true values for the given function/ equation;
Start with "Graph B" (the green graph): Upon inspection, it is clear that "(0.5 , 7)" is a point on the graph; that is, for "Graph B" ,
when "x = 0.5" , y = 7" .
Let us plug these values into the equation: y = 5(2)⁻ˣ ; to see if the equation holds true; that is, when "x = 0.5" , does "y = 7" ?
5* 2^(-0.5) = 5 * 0.7071067811865475 ;
→ 5 * (√2/2) =
3.5355339059327375;
→ 3.5355339059327375
7 .
________________________________________________So; we are left with:
Choice: [A]: "
Graph A"
{the red graph}.
________________________________________________