Question

clue #6
the graph of the function (f(x)=x) is transformed to form the graph of the function (h(x)=-\frac{1}{2}f(x)-1).
describe the transformations of function (f) that were used to created function (h).
function (f) was reflected over the (x - axis), vertically compressed, and translated up 1 unit.
function (f) was reflected over the (x - axis), vertically stretched, and translated down 1 unit.
function (f) was vertically compressed and translated down 1 unit.
function (f) was reflected over the (x - axis), vertically compressed, and translated down 1 unit.
guac greg was singing karaoke in the janitors closet, so cross off guac greg and janitors closet.
nacho nick was snacking, not scheming, so cross off nacho nick and \wanted to become taco royalty.\
taco tina was eating cereal quietly, so cross off taco tina and needed a midnight snack.
burrito bob was practicing juggling skills, so cross off burrito bob and \thought it was a prize.\

Explanation:

Step1: Analyze coefficient of \(f(x)\)

The coefficient \(-\frac{1}{2}\) in \(h(x)=-\frac{1}{2}f(x)-1\) has two - fold effect. The negative sign reflects the function \(f(x)\) over the \(x\) - axis. The \(\frac{1}{2}\) vertically compresses the function \(f(x)\) since \(|a|=\frac{1}{2}<1\) where \(a =-\frac{1}{2}\) in the transformation \(y = af(x)\).

Step2: Analyze constant term

The \(-1\) in \(h(x)=-\frac{1}{2}f(x)-1\) translates the function \(y =-\frac{1}{2}f(x)\) down 1 unit according to the transformation \(y=af(x)+k\) where \(k=-1\).

Answer:

Function \(f\) was reflected over the \(x\) - axis, vertically compressed, and translated down 1 unit.