Question

Which function represents g(x), a reflection of f(x) = 4across the x-axis?

g(x) = −4(2)x

g(x) = 4(2)−x

g(x) = −4

g(x) = 4

Answer 1

`g(x)=-4(2)^(-x)`

Explanation:

Given: The graph of f(x) (blue color)

f(x) reflection across x-axis to get g(x).

Using to find the equation of f(x)

The graph looks like a exponential decay whose y-intercept (0,4) and passing point (1,2).

`f(x)=4(2)^(-x)`

Reflection across x-axis

`y\rightarrow -y`

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

The function g(x) represents by

`g(x)=-4(2)^(-x)`

Hence, The
`g(x)=-4(2)^(-x)` is reflection of f(x) across x-axis.

Answer 2

Option C g(x) = -4

Explanation:

In the question a function f(x) =4 is given and we are required to tell the reflection g(x) of the given function.

The rule of reflection for a function says that:

f(x) -> - f(x)

So, in our case the value of function is f(x) = 4, after reflection the value across the x-axis the value will become negative i.e -4,

so the required function g(x) = - 4

Hence Option C g(x) = -4 is correct option.