1. Graph the function g(x) = [X1 + 4 as a translation of the
parent function f shown. How did the transformation
affect the domain and range?

The translation did not effect the domain

The translation effected the range

Step-by-step explanation:

The given graph represents f(x) = IxI

The domain of f(x) is {x : x ∈ R}, where R is the set of real numbers

The range of f(x) is {y : y ≥ 0}

The graph of g(x) is attached down

g(x) = IxI + 4

The domain of g(x) is {x : x ∈ R}, where R is the set of real numbers

The range of g(x) is {y : y ≥ 4}

The graph of g(x) is the image of the graph of f(x) after translate it 4 units up

∵ The translation is vertically

∴ The domain of f(x) = the domain of g(x)

∵ The domain of f(x) is {x : x ∈ R}

∴ The domain of g(x) is {x : x ∈ R}

∴ The translation did not effect the domain

∵ g(x) = f(x) + 4

∵ The range of f(x) is {y : y ≥ 0}

- Add 4 to the value 0

∴ The range of g(x) is {y : y ≥ 0 + 4}

∴ The range of g(x) is {y : y ≥ 4}

∴ The range of g(x) not equal the range of f(x)

∴ The translation effected the range

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4