Answer:
Given the function f(x)= [tex]2 (3.5)^x[/tex] is reflected across the x-axis to create g(x).
The rule of reflection across x- axis is: [tex](x,y) \rightarrow (x , -y)[/tex]
then;
[tex]f(x)=y = 2 (3.5)^x[/tex]
using the rule of reflection across x-axis;
[tex]-y =2 (3.5)^x}[/tex] or [tex]y= -2 (3.5)^x}[/tex]
therefore, the function g(x) = -[tex]2 (3.5)^x}[/tex]
Since, this g(x) is an exponential function it is of the form of [tex]ab^x[/tex] where a is the initial value.
On comparing we get ;
The initial value of g(x) is -2.
Now, to find the output for inputs of -1 and 1 in g(x);
At x = -1
[tex]g(-1) =-2(3.5)^{-1} =-2 \cdot \frac{1}{3.5} = \frac{-20}{35} = - 0.572[/tex] and
at x = 1
[tex]g(1) =-2(3.5)^1 = -2 \cdot 3.5 = -7[/tex]
