Q:

The function f(x) = 2(3.5)x is reflected across the x-axis to create g(x).The function f(x) = 2(3.5)x is reflected across the x-axis to create g(x).What is the function definition of g(x)?g(x) =–21/22 (3.5x)What is the initial value of g(x)?–3.5–202What are the outputs for inputs of –1 and 1 in g(x)?g(−1) =–7–0.570.577g(1) =–7–0.570.577

Accepted Solution

A:
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]