College Algebra 12th Edition – Ron Larson (1)

1. A ________ ________ is a quotient of polynomial functions. 2. When f (x) → ±∞ as x → a from the left or the right, x = a is a ________ ________ of the graph of f. 3. When f (x) → b as x → ±∞, y = b is a ________ ________ of the graph of f. 4. The graph of f (x) = 1∙x is a ________.

5. What feature of the graph of f (x) = ​ 9 _____ x − 3 ​ can you find by solving x − 3 = 0? 6. Is y = 4 a horizontal asymptote of the function f (x) = ​ 4x ______ x2 − 8 ​? Skills and Applications Finding the Domain of a Rational Function Find the domain of the function and discuss the behavior of f near any excluded x-values. (See Example 1.) 7. f (x) = ​ 1 _____ x − 1 ​ 8.

f (x) = ​ 4 _____ x + 3 ​ 9. f (x) = ​ ___________ x2 + 7x + 12 ​ 10. f (x) = ​ __________ x2 − 5x + 6 ​ 11. f (x) = ​ 3×2 ______ x2 − 1 ​ 12. f (x) = ​ 2x ______ x2 − 4 ​ 13. f (x) = ​ x2 + 3x + 2 __________ x2 − 2x + 1 ​ 14.

f (x) = ​ x2 + x − 20 ___________ x2 + 8x + 16 ​ Finding Vertical and Horizontal Asymptotes Find all vertical and horizontal asymptotes of the graph of the rational function. (See Example 2.) 15. f (x) = ​ 4 __ x2 ​ 16. f (x) = ​ _______ (x − 2)3 ​ 17. f (x) = ​ 5 + x _____ 5 − x ​ 18. f (x) = ​ 3 − 7x ______ 3 + 2x ​ 19. f (x) = ​ x3 ______ x2 − 1 ​ 20.

f (x) = ​ 2×2 _____ x + 1 ​ 21. f (x) = ​ −4×2 + 1 _________ x2 + x + 3 ​ 22. f (x) = ​ 3×2 + x − 5 __________ x2 + 1 ​ Finding Asymptotes and Holes Find all asymptotes and holes in the graph of the rational function. (See Examples 3 and 4.) 23. f (x) = ​ x2 − 1 __________ x2 − 2x − 3 ​ 24.

Increasing on (−∞, ∞) Decreasing on (−∞, 0) Increasing on (0, ∞) Odd function Increasing on (0, ∞) Origin symmetry Even function y-axis symmetry Greatest Integer Function Quadratic (Squaring) Function Cubic Function f(x) = ⟨x⟩ f(x) = x2 f(x) = x3 x y 1 −1 −2 −3 2 3 −3 1 2 3 f(x) = x [[ ]] x y (0, 0) f(x) = x2 −1 −2 −3 1 2 3 −1 −2 1 2 3 4 x y (0, 0) f(x) = x3 −2 −3 1 2 3 −2 −1 −3 2 3 Domain: (−∞, ∞) Domain: (−∞, ∞) Domain: (−∞, ∞) Range: the set of integers Range: [0, ∞) Range: (−∞, ∞) x-intercepts: in the interval [0, 1) Intercept: (0, 0) Intercept: (0, 0) y-intercept: (0, 0) Decreasing on (−∞, 0) Increasing on (−∞, ∞) Constant between each pair of Increasing on (0, ∞) Odd function consecutive integers Even function Origin symmetry Jumps vertically one unit at y-axis symmetry each integer value Relative minimum or vertex: (0, 0) Copyright 2027 Cengage Learning.

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