Question

Which function represents g(x), a reflection of f(x) =2/5 (10)x across the x-axis? g(x) =-2/5 (10)x g(x) =-2/5(1/10)^x g(x) =2/5(1/10)^-x g(x) =2/5 (10)-x

Answer 1

all values of f(x) will change from positive to negative if you reflect in x-axis.

So the first choice is the correct one.

Answer 2

A.
`g(x)=-(2)/(5)(10)^x`.

Explanation:

We are given the function
`f(x)=(2)/(5)(10)^x`.

Now, g(x) is obtained by reflecting the function f(x) over x-axis.

Reflection of f(x) over x-axis changes f(x) to -f(x).

So, we get,

`g(x)=-f(x)`

i.e.
`g(x)=-(2)/(5)(10)^x`

Thus, the reflected function is
`g(x)=-(2)/(5)(10)^x`.

So, option A is correct.