13. the point a(6, 4) is on the graph of the function $g(x)$. if the function is transformed into…
13. the point a(6, 4) is on the graph of the function $g(x)$. if the function is transformed into $m(x)=3g\\left2(x+1)\\right-7$, the coordinates of the image point will be $(x, y)$. the value of $x + y$ is ______.
Answer
Explanation:
Step1: Reverse horizontal stretch/compression
For the inner transformation $2(x+1)$, first solve for the new $x$-coordinate from $x' = 2(x_A + 1)$. We rearrange to find the transformed $x$: $x = \frac{x_A}{2} - 1$ Substitute $x_A=6$: $x = \frac{6}{2} - 1 = 3 - 1 = 2$
Step2: Apply vertical transformations
For the vertical transformation $3g(\cdot)-7$, calculate the new $y$-coordinate: $y = 3y_A - 7$ Substitute $y_A=4$: $y = 3\times4 - 7 = 12 - 7 = 5$
Step3: Calculate $x+y$
Add the transformed $x$ and $y$ values: $x+y = 2 + 5$
Answer:
7