The Function Y=f(x) has a domain of {xl 2 ≤ x ≤ 6, XER} and a range of {yl -4 ≤ y ≤ 8, YER} the function undergoes the transformation y=-f(1/2x) The domain and range of the transformed function are?

Question

A) domain: {xl -6 ≤ x ≤ -2, XER}  range: {yl -8 ≤ y ≤ 16, YER}

B) domain: range:{xl 4 ≤ x ≤ 12, XER} range: {yl -8 ≤ y ≤ 4, YER}

C) domain: range:{xl -12 ≤ x ≤ -4, XER} range: {yl -4 ≤ y ≤ 8, YER}

D) domain: range:{xl 1 ≤ x ≤ 3, XER} range: {yl -8 ≤ y ≤ 4, YER}

Answer 1

If the domain of f(x) is {x | x ∈ R, 2 ≤ x ≤6}, then f[(1/2)x] has been horizontally stretched by a factor of 2.

That means the domain has stretched so that 4 ≤ x ≤ 12. Based on the answer choices, you can already conclude B.

But just in case: the minus sign reflects f(x) over the x-axis. So the range is turned upside down. The highpoint 8 is reflected to -8 and the low point -4 is reflected to 4..

This graph shows a function that comes close to matching these conditions (the range is not quite correct), but is should give you the idea:

desmos.com/calculator/wjab27oewx