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Chapter 16 Study Guide Name:__________________________ 1. Graph each of the piecewise functions. a) b) d) c) e) f) 2. Evaluate each of the following in its respective piecewise function. a) 𝒇(−𝟐) = b) 𝒇(𝟕) = e) 𝒈(𝟐) = f) 𝒈(𝟐𝟓) = i) 𝒉(𝟑. 𝟓) = c) g) j) 𝒉(𝟑) = 𝒇(𝟎) = d) 𝒈(𝟑) = 𝒈(−𝟒) = h) 𝒉(𝟐) = k) 𝒉(−𝟒) = 3. Write a piecewise function for each of the graphs provided. a) b) c) 4. Graph each of the absolute value functions. a) 𝒇(𝒙) = |𝒙| − 𝟑 b) 𝒇(𝒙) = −|𝟐𝒙| + 𝟓 a) 𝟐 𝟑 𝒇(𝒙) = | 𝒙| 5. Evaluate each of the following floor and ceiling functions. ⌈𝟑. 𝟓⌉ ⌈𝟕. 𝟐⌉ ⌈−𝟓. 𝟐⌉ ⌈𝟎. 𝟑⌉ ⌊𝟑. 𝟓⌋ ⌊𝟕. 𝟐⌋ ⌊−𝟓. 𝟐⌋ ⌊𝟎. 𝟑⌋ ⌈𝟏𝟐. 𝟓⌉ ⌈𝟕. 𝟓⌉ ⌊𝟎. 𝟑𝟓⌋ ⌊−𝟕. 𝟐⌋ 6. Identify the inverse of the following situation. Wake Up -> Brush Teeth-> Get Dressed-> Drive to Work-> Start Work 7. Find the inverse for each of the following algebraically a) b) c) d) e) f) g) h) i) 8. Given the graph determine if the two function are inverses. Explain how you know. 9. Graph the function and it’s inverse function. 10. Given the following functions solve for the composition. 𝒇(𝒙) = 𝟑𝒙 + 𝟐 a) 𝒇(𝒈(𝒙)) = 𝒈(𝒙) = 𝟓𝒙 b) 𝒈(𝒇(𝒙)) = 𝒉(𝒙) = 𝒙 − 𝟕 c) 𝒈(𝒉(𝒙)) = d) 𝒉(𝒇(𝒙)) = 11. Using composition of functions determine if the two functions are inverses of each other. a) b) c) d) e) f) 12. Factor each of the following. a) 𝟗𝒙𝟐 − 𝟏𝟎𝟎 b) 𝟐𝒙𝟐 + 𝟐𝟒 + 𝟒𝟎 c) 𝟏𝟎𝒙𝟐 + 𝟏𝟕𝒙 + 𝟑 13. Solve the Quadratic. a) 𝒙𝟐 − 𝟐𝒙 + 𝟏𝟎 = 𝟎 b) 𝒙𝟐 + 𝟒𝒙 − 𝟔𝟎 = 𝟎 c) 𝒙𝟐 − 𝟔𝒙 + 𝟏 = 𝟎