Question

The function f(x) = 5()x is reflected over the y-axis. Which equations represent the reflected function? Check all that apply.

f(x) = (5)x

f(x) = (5)–x
f(x) = ()x
f(x) = 5()–x
f(x) = 5(5)x
f(x) = 5(5)–x

Answer 1

The correct option is D. f(x) = 5()-x

Explanation:

If a function f(x) is reflected over axis then the resultant equation of the function f(x) changes to f(-x)

Now, in the given problem the function is given to be : f(x) = 5()x

So, if we reflect the given function f(x) over the y- axis then the equation of the function changes to f(-x)

Hence, The required reflected equation of the given function f(x) is 5()-x

Therefore, The correct option is D. f(x) = 5()-x

Answer 2

Key term "Reflected", which is equivalent to "inverse". This means that the graph, although remains with the same points, is "reflected". Think of a mirror.
Say y = m(x). The reflected result is y = -m(x). Or in another case, y = m(-x) will be reflected to y = m(x).
Lets break this rule further. Say your point was (a,b) which is code for (x,y). If we're looking at the x-axis, the y becomes negative. Henceforth, it becomes (x,-y) and vice versa.
In this case, we're looking at the y-axis reflected, meaning, the x-value will be NEGATIVE.

Answer is C: m(x) - 5() -x This can be seen as m(x) = m(-x) as well.