Evaluate the function at the indicated values

Math 3β€”College Algebra 2.1—2.4 Homework Name: ______________________ Show all your work for full credit: 2.1 Functions Q1—Q3. Evaluate the function at the indicated values. Q1. 𝑓(π‘₯) = π‘₯ 2 βˆ’ 6, Q2. 𝑓(π‘₯) = 1βˆ’2π‘₯ 3 1 𝑓(βˆ’3), 𝑓(3), 𝑓(0), 𝑓 (2) 1 , 𝑓(2), 𝑓(βˆ’2), 𝑓 ( ) , 𝑓(π‘Ž), 𝑓(βˆ’π‘Ž), 𝑓(π‘Ž βˆ’ 1) 2 1 Q3. 𝑓(π‘₯) = π‘₯ 2 + 2π‘₯, 𝑓(0), 𝑓(3), 𝑓(βˆ’3), 𝑓(π‘Ž), 𝑓(βˆ’π‘₯), 𝑓 (π‘Ž) Q4β€”Q5. Evaluate the piecewise defined function at the indicated values. π‘₯2 Q4. 𝑓(π‘₯) = { π‘₯+1 𝑖𝑓 π‘₯ < 0 𝑖𝑓 π‘₯ β‰₯ 0 𝑓(βˆ’2), 𝑓(βˆ’1), 𝑓(0), 𝑓(1), 𝑓(2) π‘₯ 2 βˆ’ 2π‘₯ 𝑖𝑓 π‘₯ ≀ βˆ’1 Q5. 𝑓(π‘₯) = { π‘₯ 𝑖𝑓 βˆ’ 1 < π‘₯ ≀ 1 βˆ’1 𝑖𝑓 π‘₯ > 1 𝑓(βˆ’4), 3 𝑓 (βˆ’ ) , 2 𝑓(βˆ’1), Q6β€”Q9. Find the domain of the function 1 Q6. 𝑓(π‘₯) = π‘₯βˆ’3 Q7. 𝑓(𝑑) = βˆšπ‘‘ + 1 Q8. 𝑔(π‘₯) = √1 βˆ’ 2π‘₯ Q9. 𝑓(π‘₯) = 3π‘₯ 1 𝑓(0), 𝑓(25) 2.2 Graphs of a function Q1β€”Q4. Sketch a graph of the function by first making a table of values. Q1. 𝑓(π‘₯) = βˆ’π‘₯ + 3, βˆ’3≀π‘₯ ≀3 Q2. 𝑓(π‘₯) = βˆ’π‘₯ 2 Q3. 𝑓(π‘₯) = 1 + √π‘₯ Q4. 𝑓(π‘₯) = | 2π‘₯| Q5β€”Q7. Sketch a graph of the piecewise defined function. 3 Q5. 𝑓(π‘₯) = { π‘₯βˆ’1 π‘₯ Q6. 𝑓(π‘₯) = { π‘₯+1 𝑖𝑓 π‘₯ < 2 𝑖𝑓 π‘₯ β‰₯ 2 𝑖𝑓 π‘₯ ≀ 0 𝑖𝑓 π‘₯ > 0 4 𝑖𝑓 π‘₯ < βˆ’2 Q7. 𝑓(π‘₯) = {π‘₯ 𝑖𝑓 βˆ’ 2 ≀ π‘₯ ≀ 2 βˆ’π‘₯ + 6 𝑖𝑓 π‘₯ > 2 2 Q8β€”Q10. Determine whether the equation defines 𝑦 as a function of π‘₯ Q8. 3π‘₯ βˆ’ 5𝑦 = 7 Q9. 2π‘₯ βˆ’ 4𝑦 2 = 4 Q10. 2|π‘₯| + 𝑦 = 0 2 2.3 Getting information from the graph of a function Q1. The graph of a function β„Ž is given a) b) c) d) e) Find β„Ž(βˆ’2), β„Ž(0), β„Ž(2) and β„Ž(3) Find the domain and range of β„Ž Find the values of π‘₯ for which β„Ž(π‘₯) = 3 Find the values of π‘₯ for which β„Ž(π‘₯) ≀ 3 Find the net change in h between π‘₯ = βˆ’3 and π‘₯ = 3 Q2. Graphs of the functions 𝑓 and 𝑔 are given. a) b) c) d) e) Which is larger, 𝑓(0) π‘œπ‘Ÿ 𝑔(0)? Which is larger, 𝑓(βˆ’3) or 𝑔(βˆ’3)? For which values of π‘₯ is 𝑓(π‘₯) = 𝑔(π‘₯)? Find the values of π‘₯ for which 𝑓(π‘₯) ≀ 𝑔(π‘₯) Find the values of π‘₯ for which 𝑓(π‘₯) > 𝑔(π‘₯) 3 Q3β€”Q5. A function 𝑓 is given. (π‘Ž) sketch a graph of 𝑓 (b) use the graph to find the domain and range of 𝑓 Q3. 𝑓(π‘₯) = 2π‘₯ + 3 Q4. 𝑓(π‘₯) = π‘₯ βˆ’ 2 βˆ’2 ≀ π‘₯ ≀ 5 Q5. 𝑓(π‘₯) = π‘₯ 2 βˆ’ 1, βˆ’3 ≀ π‘₯ ≀ 3 Q6β€”Q7. The graph of the function 𝑓 is given. Use the graph to estimate the following a) The domain and range of 𝑓 b) The intervals on which 𝑓 is increasing and on which 𝑓 is decreasing. Q6. Q7. Q8. A function 𝑓 is given. a) Graph the function b) Find the domain and range of 𝑓 c) State approximately the intervals on which 𝑓 is increasing and on which 𝑓 is decreasing. d) Find all local maximum and local minimum values 𝑓(π‘₯) = π‘₯ 2 βˆ’ 5π‘₯ 4 2.4 Average rate of change of a function Q1β€”Q5. A function is given. Determine (a) the net change and (b) the average rate of change between the given values of the variable. Q1. 𝑓(π‘₯) = 3π‘₯ βˆ’ 2 3 π‘₯ = 2, π‘₯ = 3 Q2. β„Ž(𝑑) = βˆ’π‘‘ + 2 𝑑 = βˆ’4, 𝑑 = 1 Q3. β„Ž(𝑑) = 2𝑑 2 βˆ’ 𝑑 𝑑 = 3, 𝑑 = 6 Q4. 𝑓(π‘₯) = π‘₯ 3 βˆ’ 4π‘₯ 2 1 Q5. 𝑔(π‘₯) = π‘₯ π‘₯ = 0, π‘₯ = 10 π‘₯ = 1, π‘₯ = π‘Ž 5
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