Write the Transformed equation given the following transformations of Translated left 6 and up 3

To apply the given transformations—**translated left by 6 units** and **up by 3 units**—to an original equation, you can follow these general steps. Let's assume the original equation is in the form: \[ y = f(x) \] ### Step 1: Translate Left by 6 Units Translating the graph of the function **left by 6 units** involves replacing \( x \) with \( x + 6 \). This shifts every point on the graph 6 units to the left. \[ y = f(x + 6) \] ### Step 2: Translate Up by 3 Units Next, to translate the graph **up by 3 units**, you add 3 to the entire function. This shifts every point on the graph 3 units upward. \[ y = f(x + 6) + 3 \] ### Combined Transformation Combining both transformations, the **transformed equation** is: \[ y = f(x + 6) + 3 \] ### Example **Original Equation:** \[ y = x^2 \] **Transformed Equation (translated left 6 and up 3):** \[ y = (x + 6)^2 + 3 \] This transformation shifts the parabola \( y = x^2 \) 6 units to the left and 3 units upward. --- **Summary:** Given an original equation \( y = f(x) \), the transformed equation after translating left by 6 units and up by 3 units is: \[ y = f(x + 6) + 3 \]