Question

Which function represents a reflection of f(x) = 5(0.8)^x across the x-axis?

g(x) = 5(0.8)^–x
g(x) = –5(0.8)^x
g(x) = (0.8)^x
g(x) = 5(–0.8)^x

Answer 1

B. g(x) = –5(0.8)^x

Step-by-step explanation:

We have the function,
`f(x) = 5(0.8)^x`.

It is required to reflect the function about x-axis.

Now, as we know,

Reflection across x-axis will flip the graph of the function and the function
`f(x)` becomes
`-f(x)`.

So, the reflection of
`f(x) = 5(0.8)^x` across x-axis will give the function
`f(x) = -5(0.8)^x`

So, we see that,

Option B i.e.
`g(x) = -5(0.8)^x` is correct.

Answer 2

Answer: The correct option is second.

Step-by-step explanation:

The given function is,

`f(x)=5(0.8)^x`

If we graph a function is f(x), then its coordinates is defined as (x,f(x)).

When the graph of f(x) is reflect across the x-axis, then the the x-coordinate remains the same and the sign of y-coordinate is changed. It means after reflecting across the x-axis,

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

The given given equation can be written as,

`y=5(0.8)^x`

To find the equation of the graph after reflection across the x-axis multiply both sides by -1.

`-y=-5(0.8)^x`

Because f(x)=y and g(x)=-y.

`g(x)=-5(0.8)^x`

Therefore the second option is correct and the graph of both function is given below.