The parent function is x^3 (black). We can change this function by using translations. To translate vertically we must add to y. Here, I translated by 1 and got y=x^3 +1 (red). To translate horizontally I shifted 5 to the right and subtracted from x, resulting in (x-5)^3 (blue). Combining both will result in (x-5)^3+1 (green). As for reflections, I set x to -x. I got a reflection across the x-axis using y=-x^3 (purple). We can also combine reflections and translations, as seen in y=-(x-5)^3-1 (Sharpie). There will not be a reflection across the y-axis on the original function since that would have no effect.
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