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- f(x) = 2x² +5; Translation 2 units down and 3 units left

write a g function whose graph represents the indicated transformation of the graph of f

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Answer: g(x)= 2x² - 12x + 21.

Step-by-step explanation: To translate the graph of the function f(x) = 2x² + 5, 2 units down and 3 units left, we need to adjust the equation to incorporate these translations.

To move the graph 2 units down, we subtract 2 from the original function:

f(x) - 2 = 2x² + 5 - 2

To move the graph 3 units to the left, we substitute (x - 3) for x in the function:

f(x - 3) - 2 = 2(x - 3)² + 5 - 2

Simplifying further, we have:

f(x - 3) - 2 = 2(x² - 6x + 9) + 3

Expanding and combining like terms, we get:

f(x - 3) - 2 = 2x² - 12x + 18 + 3

Combining like terms again, we have:

f(x - 3) - 2 = 2x² - 12x + 21

Therefore, the function g(x) that represents the indicated translation of the graph of f is:

g(x) = 2x² - 12x + 21.

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