Question

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

Answer 1

Answer:

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

$g(-1) =-2(3.5)^{-1} =-2 \cdot \frac{1}{3.5} = \frac{-20}{35} = - 0.572$  and

at x = 1

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

Answer 2

g(x)=-2 (3.5)x

the initial value is -2

g(-1)=-0.57

g(1)=-7