Question
Write the function in its final position. F(x)=x^3 first move 2 units downward, then 3 units to the left and finally flipped over the y-axis
Answers
GPT 3.5
Starting with the function f(x) = x^3, let's go through each transformation step by step.
1. Moving 2 units downward: To move the function 2 units downward, we subtract 2 from the original function value, resulting in f(x) = x^3 - 2.
2. Moving 3 units to the left: To move the function 3 units to the left, we replace x with (x + 3) to shift the function horizontally. Now our function becomes f(x) = (x + 3)^3 - 2.
3. Flipping over the y-axis: To flip the function over the y-axis, we replace x with -x, which is equivalent to reflecting it across the y-axis. Thus, our final function is f(x) = (-x + 3)^3 - 2.
Therefore, the given function f(x) = x^3 after moving 2 units downward, 3 units to the left, and flipped over the y-axis is f(x) = (-x + 3)^3 - 2.
1. Moving 2 units downward: To move the function 2 units downward, we subtract 2 from the original function value, resulting in f(x) = x^3 - 2.
2. Moving 3 units to the left: To move the function 3 units to the left, we replace x with (x + 3) to shift the function horizontally. Now our function becomes f(x) = (x + 3)^3 - 2.
3. Flipping over the y-axis: To flip the function over the y-axis, we replace x with -x, which is equivalent to reflecting it across the y-axis. Thus, our final function is f(x) = (-x + 3)^3 - 2.
Therefore, the given function f(x) = x^3 after moving 2 units downward, 3 units to the left, and flipped over the y-axis is f(x) = (-x + 3)^3 - 2.