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

Given:

The given function is $f(x)=\frac{3}{7}(2)^{x}$

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

$-y=\frac{3}{7}(2)^{x}$

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

$y=-\frac{3}{7}(2)^{x}$

This can be written as

$g(x)=-\frac{3}{7}(2)^{x}$

Hence, the reflection of the function over the x - axis is $g(x)=-\frac{3}{7}(2)^{x}$

Thus, Option A is the correct answer.

Answer 2

Answer:

a

Step-by-step explanation:

edge 2021