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 \( y=f(x+8) \) ? The \( x \)-intercepts of the graph of \( y=f(x+8) \) are \( -14,-11 \). (Use a comma to separate answers as needed.) (b) What are the \( x \)-intercepts of the graph of \( y=f(x-7) \) ? The \( x \)-intercepts of the graph of \( y=f(x-7) \) are (Use a comma to separale answers as needed.)
Ask by Huang Lambert. in the United States
Mar 17,2025
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Answer
(a) The \( x \)-intercepts of \( y = f(x + 8) \) are \( -14, -11 \).
(b) The \( x \)-intercepts of \( y = f(x - 7) \) are \( 1, 4 \).
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The Deep Dive
To find the \( x \)-intercepts of the graph of \( y=f(x-7) \), we need to determine where this function equals zero, which occurs when \( x-7 \) equals the original \( x \)-intercepts. Given the original \( x \)-intercepts of \( -6 \) and \( -3 \), we set: 1. \( x - 7 = -6 \) → \( x = 1 \) 2. \( x - 7 = -3 \) → \( x = 4 \) Thus, the \( x \)-intercepts of the graph of \( y=f(x-7) \) are \( 1, 4 \).