Question

The function f(x) = 2(3.5)' is reflected across the x-axis to create g(x).

What is the function definition of g(x)?
g(x) = (3.59
What is the initial value of g(x)?
What are the outputs for inputs of -1 and 1 in g(x)?
9(-1) =
g(1) =

Answer 1

The function g(x) is a reflection of f(x) = 2(3.5)^x across the x-axis and is defined as g(x) = -2(3.5)^x. The initial value of g(x) is -2. The outputs for g(-1) and g(1) are approximately -0.5714 and -7, respectively.

Step-by-step explanation:

Reflection of f(x)

The given function f(x) = 2(3.5)^x when reflected across the x-axis will change the sign of its outputs. This means that for the function g(x), which is the reflection of f(x), the outputs will be the negatives of f(x)'s outputs. Hence, the definition of g(x) would be:

g(x) = -2(3.5)^x

The initial value of g(x), which can also be referred to as the y-intercept, is the output when x = 0. Therefore, the initial value of g(x) is:

g(0) = -2(3.5)^0 = -2(1) = -2

Now, we can find the outputs for inputs of -1 and 1. For g(-1), we get:

g(-1) = -2(3.5)^{-1} = -2(1/3.5) = -2/3.5 = -4/7 ≈ -0.5714

And for g(1), we have:

g(1) = -2(3.5)^1 = -2(3.5) = -7

Answer 2

g(x)=-2 (3.5)x

the initial value is -2

g(-1)=-0.57

g(1)=-7