Subjects algebra

Function Transformation 1B5896

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1. The problem states that the point $(-4, -3)$ lies on the graph of $y = f(x)$. We need to find which point lies on the graph of $y = f(x) + 2$. 2. The transformation $y = f(x) + 2$ means we add 2 to the $y$-value of every point on the original graph. 3. Since $(-4, -3)$ is on $y = f(x)$, the corresponding point on $y = f(x) + 2$ will be $(-4, -3 + 2) = (-4, -1)$. 4. Checking the options: - $(-2, -3)$: $x$ changed, so no guarantee. - $(-6, -3)$: $x$ changed, so no guarantee. - $(-4, -1)$: $x$ same, $y$ increased by 2, matches our transformation. - $(0, 2)$: $x$ changed, no guarantee. 5. Therefore, the point $(-4, -1)$ must be on the graph of $y = f(x) + 2$. Final answer: $\boxed{(-4, -1)}$