Solve the following equations

\f\fa) Explain why this relation is a function. Why is it important for this to be so? b) State the domain and range of the function. \f\f\fc) In part (b), what do you notice about the answers to parts (v) and (vi)? Explain why this happens- 10. The graph at the right shows x) = 2(x E")2 - 1. n a) EvaluateZ). b) What does f(2) represent an the graph off? c) State the domain and range of the relation. d) How do you know that f is a function from its graph? 13. As a mental arithmetic exercise, a teacher asked her students to think of a number, triple it, and subtract the resulting number from 24. Finally, they were asked to multiply the resulting difference by the number they rst thought of. it) Use Function notation to express the nal answer in terms of the original number. b} Determine the result of choosing numbers 3. 5, and 10. c) Determine the maximum result possible. 14. The seeond span of the Bluewater Bridge in Sarnia, Ontario, is supported by two parabolic arches. Each arch is set in concrete foundations that are on opposite sides of the St. Clair River. The arches are 281 m apart. The top of each arch rises 71 m above the river. Write a function to model the arch. 15. :1) Graph the mcrionx) = 3(x - 1)2 4. b) What does f( - 1) represent on the graph? Indicate on the graph how you would nd l). c) Use the equation to determine i)f(2) '1'\") ii) #8) *7 m)f(1*x) 16. Letx) = x2 + 2x 15. Determine the values ofx for which 1) f(x) = 0 5) f(x) = -12 c) f(x) = 16 11. Lctx) = 3x + l and g(x) = 2 3:. Determine values Fora such that 3] f0!) = 3(a) b) a') = 0\") \fl' Im'llll'u 4. The grades and numbers of credits for students are listed. I1! I) Write a list ofordercd pairs and create a mapping diagram For the relation between ' students and grades ' grades and numbers of credits ' students and numbers of credits b) State the domain and range ofeach relation in part (a). c) Which relations in part (a) are functions? Explain. 6. Describe the graphs of the relations y = 3 and x = 3. Are these relations functions? Explain. 7. Identify each type of reiation and predict whether it is a Function. Then graph each Emotion and use the vertical-fine test to determine whether your prediction was correct. \f3. Identify which of the relations in questions 1 and 2 are mctiens. 4. Determine the domain and range ofthe functionx) = 2(x l)2 3 by sketching its graph. \f