Understanding Function Transformation

The video tutorial explains how to determine the function f(x) given that f(x+3) equals 4x+5 for all x. It involves rewriting the function rule for f(x+3) to match the input on the right side, simplifying the expression, and then determining f(x) by replacing x+3 with x. The final result is f(x) equals 4x minus 7.

What is the initial equation given for f(x + 3)?

• f(x + 3) = 4x + 3

• f(x + 3) = 5x + 4

• f(x + 3) = 3x + 4

• f(x + 3) = 4x + 5

How do we rewrite 4x in terms of (x + 3)?

• 4x - 3

• 4(x - 3)

• 4(x + 3)

• 4x + 3

What operation is performed to eliminate the extra 12 in the expression?

• Subtract 12

• Add 12

• Divide by 12

• Multiply by 12

What is the final expression for f(x) after simplification?

• f(x) = 4x - 5

• f(x) = 4x + 5

• f(x) = 4x - 7

• f(x) = 4x + 7

What is the purpose of replacing x + 3 with x in the final step?

• To find the function f(x)

• To simplify the equation

• To solve for x

• To eliminate x