Question

PLEASE HELP!!!!

The function f(x)=−4x+3 is a linear function. Let g(x) represent f(x) after a horizontal translation 2 units to the left.

What is the equation for g(x) ?



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Answer 1

in short, a horizontal translation, means f("x + some number"),

now, that number is 2, and is to the left, so that means f(x + 2)


`\bf \begin{cases} f(x)=-4x+3\\ g(x)=f(x+2) \end{cases} \\\\\\ f(x+2)=-4(x+2)+3\implies f(x+2)=-4x-8+3 \\\\\\ f(x+2)=-4x-5\impliedby g(x)`