1. Splash Screen

2. Determine whether the relation y 2 – 4x = 3 represents y as a function of x.
A. yes
B. no
5–Minute Check 1

3. Describe the end behavior of f (x) = 4x 4 + 2x – 8.
5–Minute Check 2

4. Identify the parent function f (x) of g (x) = 2|x – 3| + 1
Identify the parent function f (x) of g (x) = 2|x – 3| + 1. Describe how the graphs of g (x) and f (x) are related.
A. f (x) = | x |; f (x) is translated 3 units right, 1 unit up and expanded vertically to graph g (x).
B. f (x) = | x |; f (x) is translated 3 units right, 1 unit up and expanded horizontally to graph g (x).
C. f (x) = | x |; f (x) is translated 3 units left, 1 unit up and expanded vertically to graph g (x).
D. f (x) = | x |; f (x) is translated 3 units left, 1 unit down and expanded horizontally to graph g (x).
5–Minute Check 3

5. Evaluate f (2x) if f (x) = x 2 + 5x + 7.
A. 2x x + 7
B. 2x x 2 + 7
C. 4x x + 7
D. 4x 2 + 7x + 7
5–Minute Check 5

6. power function monomial function radical function extraneous solution
Vocabulary

7. Key Concept 1

8. Analyze Monomial Functions
A. Graph and analyze Describe the domain, range, intercepts, end behavior, continuity, and where the function is increasing or decreasing.
Evaluate the function for several x-values in its domain. Then use a smooth curve to connect each of these points to complete the graph.
Example 1

9. Answer: D = (–∞, ∞); R = [0, ∞); intercept: 0;
Analyze Monomial Functions
Answer: D = (–∞, ∞); R = [0, ∞); intercept: 0;
continuous for all real numbers; decreasing: (–∞, 0) , increasing: (0, ∞)
Example 1

10. Analyze Monomial Functions
B. Graph and analyze f (x) = –x 5. Describe the domain, range, intercepts, end behavior, continuity, and where the function is increasing or decreasing.
Example 1

11. Analyze Monomial Functions
Answer: D = (–∞, ∞); R = (–∞, ∞); intercept: 0; continuous for all real numbers; decreasing: (–∞, 0)
Example 1

12. B. increasing: (–∞, 0) , decreasing: (0, ∞) C. decreasing: (–∞, ∞)
Describe where the graph of the function f (x) = 2x 4 is increasing or decreasing.
A. increasing: (–∞, ∞)
B. increasing: (–∞, 0) , decreasing: (0, ∞)
C. decreasing: (–∞, ∞)
D. increasing: (–∞, 0), decreasing: (0, ∞)
Example 1

13. Functions with Negative Exponents
A. Graph and analyze f (x) = 2x – 4. Describe the domain, range, intercepts, end behavior, continuity, and where the function is increasing or decreasing.
Example 2

14. Answer: D = (– ∞, 0)  (0, ∞); R = (0, ∞); ;
Functions with Negative Exponents
Answer: D = (– ∞, 0)  (0, ∞); R = (0, ∞); ;
infinite discontinuity at x = 0; increasing: (–∞, 0), decreasing: (0, ∞);
Example 2

15. Functions with Negative Exponents
B. Graph and analyze f (x) = 2x –3. Describe the domain, range, intercepts, end behavior, continuity, and where the function is increasing or decreasing.
Example 2

16. D = (–∞, 0)  (0, ∞); R = (–∞, 0)  (0, ∞);
Functions with Negative Exponents
D = (–∞, 0)  (0, ∞); R = (–∞, 0)  (0, ∞);
intercept: none;
end behavior:
continuity: infinite discontinuity at x = 0;
decreasing: (–∞, 0) and (0, ∞)
Example 2

17. Answer: D = (–∞, 0)  (0, ∞); R = (–∞, 0)  (0, ∞);
Functions with Negative Exponents
Answer: D = (–∞, 0)  (0, ∞); R = (–∞, 0)  (0, ∞);
; infinite discontinuity at x = 0; decreasing: (–∞, 0) and (0, ∞)
Example 2

18. Describe the end behavior of the graph of f (x) = 3x –5.
Example 2

19. Rational Exponents
A. Graph and analyze Describe the domain, range, intercepts, end behavior, continuity, and where the function is increasing or decreasing.
Example 3

20. Rational Exponents
Answer: D = [0, ∞); R = [0, ∞); intercept: 0; ; continuous on (0, ∞); increasing: (0, ∞)
Example 3

21. Rational Exponents
B. Graph and analyze Describe the domain, range, intercepts, end behavior, continuity, and where the function is increasing or decreasing.
Example 3

22. Rational Exponents
Answer: D = (–∞, 0) (0, ∞); R = (0, ∞); ; infinite discontinuity at x = 0; increasing: (–∞, 0), decreasing: (0, ∞)
Example 3

23. Describe the continuity of the function .
A. continuous for all real numbers
B. continuous on and
C. continuous on
D. continuous on
Example 3