Question

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

Answer 1

Answer:

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.

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.