Question

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)?

–3.5–202

What are the outputs for inputs of –1 and 1 in g(x)?

g(−1) =–7–0.570.577

g(1) =–7–0.570.577

Answer 1

Explanation:

1. g(x)=-2 (3.5x)

2. Value of g(x)= -2

3. -1= -0.57

4. 1= -7

Answer 2

Given the function f(x)=
`2 (3.5)^x` is reflected across the x-axis to create g(x).

The rule of reflection across x- axis is:
`(x,y) \rightarrow (x , -y)`

then;

`f(x)=y = 2 (3.5)^x`

using the rule of reflection across x-axis;

`-y =2 (3.5)^x}` or
`y= -2 (3.5)^x}`

therefore, the function g(x) = -
`2 (3.5)^x}`

Since, this g(x) is an exponential function it is of the form of
`ab^x` 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

`g(-1) =-2(3.5)^(-1) =-2 \cdot (1)/(3.5) = (-20)/(35) = - 0.572` and

at x = 1

`g(1) =-2(3.5)^1 = -2 \cdot 3.5 = -7`