Write the function in vertex form, and identify its vertex. g(x) = 5x2 - 50x + 128
1 answer:
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Answer:
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
