Question

Which function represents a reflection of f(x) = Three-sevenths(2)x over the x-axis?

g(x) = –Three-sevenths(2)x
g(x) = Three-sevenths(–2)x
g(x) = Three-sevenths (one-half)–x
g(x) = Seven-thirds(2)–x

Answer 1

a

Explanation:

edge 2021

Answer 2

Given:

The given function is
`f(x)=(3)/(7)(2)^(x)`

We need to determine the reflection of f(x) over the x - axis

Reflection over x - axis:

The translation rule to reflect over the x - axis is given by

`(x, y) \rightarrow(x,-y)`

Thus, applying the rule, the function becomes

`-y=(3)/(7)(2)^(x)`

Multiplying both sides of the equation by -1, we have;

`y=-(3)/(7)(2)^(x)`

This can be written as

`g(x)=-(3)/(7)(2)^(x)`

Hence, the reflection of the function over the x - axis is
`g(x)=-(3)/(7)(2)^(x)`

Thus, Option A is the correct answer.