1. The problem asks to sketch the graph of $$y = f(-x + 4)$$ given the graph of $$y = f(x)$$. 2. The transformation inside the function argument $$f(-x + 4)$$ can be rewritten as $$f(-(x - 4))$$. 3. This means we first shift the graph of $$f(x)$$ horizontally by 4 units to the right (because of $$x - 4$$), then reflect it across the y-axis (because of the negative sign in front of $$x$$). 4. Step-by-step: - Horizontal shift: Replace $$x$$ by $$x - 4$$ shifts the graph 4 units to the right. - Reflection: Replace $$x$$ by $$-x$$ reflects the graph about the y-axis. 5. So, to sketch $$y = f(-x + 4)$$: - Take the original graph of $$f(x)$$. - Shift it 4 units to the right. - Reflect the shifted graph about the y-axis. 6. For example, if a point on $$f(x)$$ is $$(a, f(a))$$, then on $$y = f(-x + 4)$$ the corresponding point is found by solving $$-x + 4 = a$$, which gives $$x = 4 - a$$, so the point is $$(4 - a, f(a))$$. 7. This means the graph is flipped horizontally and shifted right by 4 units. 8. The final sketch will have the shape of $$f(x)$$ reversed left-to-right and moved 4 units right.