Question

Choose the correct transformation of the graph f(x) = |x - 8| +3 .

The graph of f(x) =x| is shifted to the left 8 units, down 3 units.
The graph of f(x) =x| is shifted to the right 8 units, down 3 units.
The graph of f(x) =x| is shifted to the left 8 units, up 3 units.
The graph of f(x) =x| is shifted to the right 8 units, up 3 units.

Answer 1

The graph of f(x) = |x| is shifted to the right 8 units, up 3 units.

Explanation:

f(x) + n - shift the graph of f(x) n units up

f(x) - n - shift the graph of f(x) n units down

f(x - n) - shift the graph of f(x) n units to the right

f(x + n) - shift the graph of f(x) n units to the left

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We have g(x) = |x - 8| + 3

f(x) = |x| → f(x - 8) = |x - 8| shift the graph 8 units to the right

f(x - 8) + 3 → |x - 8| + 3 shift the graph 3 unit up