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7. Determine the end behavior of f(x) = -2/x - 4 -8 X → o f(x) → -0 X → o f(x) → -00 В. X → o f(x) → ∞ С. D. А. X → -00 f(x)→ 0 X → 2 f(x) → 8 х> -4 f(x) —> -8 X → o f(x) →→ -0 X → 4 f(x) → -8

7. Determine the end behavior of f(x) = -2/x - 4 -8 X → o f(x) → -0 X → o f(x) → -00 В. X → o f(x) → ∞ С. D. А. X → -00 f(x)→ 0 X → 2 f(x) → 8 х> -4 f(x) —> -8 X → o f(x) →→ -0 X → 4 f(x) → -8

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Question 7: Determine the end behavior of \( f(x) = -2 \sqrt{x - 4} - 8 \)** **Options:** - **A.** As \( x \to \infty \), \( f(x) \to -\infty \); as \( x \to -\infty \), \( f(x) \to \infty \) - **B.** As \( x \to \infty \), \( f(x) \to -\infty \); as \( x \to 2 \), \( f(x) \to 8 \) - **C.** As \( x \to \infty \), \( f(x) \to \infty \); as \( x \to -4 \), \( f(x) \to -8 \) - **D.** As \( x \to \infty \), \( f(x) \to -\infty \); as \( x \to 4 \), \( f(x) \to -8 \) **Analysis:** Consider the function \( f(x) = -2 \sqrt{x - 4} - 8 \). As \( x \) increases without bound (i.e., \( x \to \infty \)), \( \sqrt{x - 4} \) also increases, but the overall expression due to the negative sign in front of the square root and the constant subtraction will trend towards negative infinity. For \( x = 4 \), the expression inside the square root becomes zero, and hence \( f(x) = -8 \). As \( x \to 4 \), \( f(x) \) tends towards -8. Thus, option **D** accurately describes this behavior.
Transcribed Image Text:**Question 7: Determine the end behavior of \( f(x) = -2 \sqrt{x - 4} - 8 \)** **Options:** - **A.** As \( x \to \infty \), \( f(x) \to -\infty \); as \( x \to -\infty \), \( f(x) \to \infty \) - **B.** As \( x \to \infty \), \( f(x) \to -\infty \); as \( x \to 2 \), \( f(x) \to 8 \) - **C.** As \( x \to \infty \), \( f(x) \to \infty \); as \( x \to -4 \), \( f(x) \to -8 \) - **D.** As \( x \to \infty \), \( f(x) \to -\infty \); as \( x \to 4 \), \( f(x) \to -8 \) **Analysis:** Consider the function \( f(x) = -2 \sqrt{x - 4} - 8 \). As \( x \) increases without bound (i.e., \( x \to \infty \)), \( \sqrt{x - 4} \) also increases, but the overall expression due to the negative sign in front of the square root and the constant subtraction will trend towards negative infinity. For \( x = 4 \), the expression inside the square root becomes zero, and hence \( f(x) = -8 \). As \( x \to 4 \), \( f(x) \) tends towards -8. Thus, option **D** accurately describes this behavior.
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