Suppose that the \( x \)-intercepts of the graph of \( y=f(x) \) are -6 and -3 (a) What are the \( x \)-intercepts of the graph of \( y=f(x+8) \) ? The \( x \)-intercepts of the graph of \( y=f(x+8) \) are \( -14,-11 \). (Use a comma lo separate answers as needed.) (b) What are the \( x \)-intercepts of the graph of \( y=1(x-7) \) ? The \( x \)-intercepts of the graph of \( ~ \) \( =f(x-7) \) are 1,4 (Use a comma to separale answers as needed.) (c) What ore the \( x \)-intercepts of the graph of \( y=31(x) \) ? The \( x \)-iniercepts of the graph of \( y=3 t(x) \) are \( -6,-3 \). (Use a comma to separale answers as needed.) (d) What are tho \( x \)-intercepts of the graph of \( y=f(-x) \) ? The \( x \)-intercepts of the graph of \( y=f(-x) \) are \( \square \). (Use a comma to sdarate answers as needed.)
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When transforming the function \( f(x) \) into \( f(-x) \), the \( x \)-intercepts undergo a reflection across the \( y \)-axis. This means if the original \( x \)-intercepts are \( -6 \) and \( -3 \), the new \( x \)-intercepts will switch signs to become \( 6 \) and \( 3 \). So, for part (d), the \( x \)-intercepts of the graph of \( y=f(-x) \) are \( 6, 3 \). Don’t forget that reflections can change not only the position but also the interpretation of data! Understanding how transformations affect functions can help build a solid foundation in algebra and precalculus. Be sure to visualize these changes with graphs to truly grasp the concepts!
