Question

Write a function g whose graph represents the indicated transformation of the graph of f.

Answer 1

Step-by-step explanation:

I guess this means a reflection across the x-axis.

what does that mean ?

imagine the line of the x-axis is a mirror.

everything that is originally above the x-axis, is now below the x-axis.

and everything that is originally below the x-axis, is now above it.

as with an actual mirror, the closer something is originality to the mirror the closer it also appears to be in the mirrored image.

how do we do this in math ?

well, a functional value of e.g. 1 turns into -1.

e.g. 2 turns into -2.

but also e.g. -3 turns into 3.

in other words, we only need to flip the sign of the functional result values.

how do we do this ?

by multiplying the whole original functional value by -1.

and therefore,

g(x) = f(x) × -1 = (1/2 × x - 3) × -1 = -x/2 + 3