Question
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 \( y=1(x+8) \) ? The \( x \)-intercepls of the graph of \( y=f(x+8) \) are (Use a comma to separate answers as needed.)
Ask by Cruz Reed. in the United States
Mar 17,2025
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Answer
The \( x \)-intercepts of the graph of \( y = f(x + 8) \) are -14 and -11.
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The Deep Dive
The \( x \)-intercepts of the graph of \( y=f(x) \) are the values of \( x \) where \( f(x) = 0 \). Since the \( x \)-intercepts of \( y=f(x) \) are -6 and -3, for the function \( y=f(x+8) \), we need to find where \( f(x+8) = 0 \). Setting \( x+8 = -6 \) gives \( x = -14 \) and setting \( x+8 = -3 \) gives \( x = -11 \). Therefore, the \( x \)-intercepts of the graph of \( y=f(x+8) \) are -14 and -11. So, the answer is: **-14, -11.**