The transformed equation h(x) = 3x + 3 results from a vertical stretch of 3 applied to the original function and a 3-unit downward shift from the transformation function.
To find the transformed equation for 3g(x), let's first recall the original functions: f(x) = 2x + 1 and g(x) = x + 2. The transformation applied to g(x) is a shift of 3 units down.
Starting with g(x), we can express 3g(x) as 3(x + 2). Distributing the 3 gives 3x + 6. Now, considering the downward shift, we subtract 3 units from this expression, resulting in 3x + 3.
Thus, the transformed equation for 3g(x) is h(x) = 3x + 3. This equation represents a vertical stretch by a factor of 3 from the original function f(x) and a shift of 3 units down from the transformation g(x).
In summary, the transformed equation h(x) = 3x + 3 is obtained by applying a vertical stretch to the original function f(x) = 2x + 1 and shifting it 3 units down from the transformation g(x) = x + 2.
The question probable may be:
Given the functions "f(x) = 2x + 1" and "g(x) = x + 2," where "g(x)" is a transformation of "f(x)" representing a shift of 3 units down, determine the transformed equation for "3g(x)" and label it as "h(x)." Express your answer in simplified form, using integers or fractions as needed.