# 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. π(π₯) = π₯ 2 β 6, Q2. π(π₯) = 1β2π₯ 3 1 π(β3), π(3), π(0), π (2) 1 , π(2), π(β2), π ( ) , π(π), π(βπ), π(π β 1) 2 1 Q3. π(π₯) = π₯ 2 + 2π₯, π(0), π(3), π(β3), π(π), π(βπ₯), π (π) Q4βQ5. Evaluate the piecewise defined function at the indicated values. π₯2 Q4. π(π₯) = { π₯+1 ππ π₯ < 0 ππ π₯ β₯ 0 π(β2), π(β1), π(0), π(1), π(2) π₯ 2 β 2π₯ ππ π₯ β€ β1 Q5. π(π₯) = { π₯ ππ β 1 < π₯ β€ 1 β1 ππ π₯ > 1 π(β4), 3 π (β ) , 2 π(β1), Q6βQ9. Find the domain of the function 1 Q6. π(π₯) = π₯β3 Q7. π(π‘) = βπ‘ + 1 Q8. π(π₯) = β1 β 2π₯ Q9. π(π₯) = 3π₯ 1 π(0), π(25) 2.2 Graphs of a function Q1βQ4. Sketch a graph of the function by first making a table of values. Q1. π(π₯) = βπ₯ + 3, β3β€π₯ β€3 Q2. π(π₯) = βπ₯ 2 Q3. π(π₯) = 1 + βπ₯ Q4. π(π₯) = | 2π₯| Q5βQ7. Sketch a graph of the piecewise defined function. 3 Q5. π(π₯) = { π₯β1 π₯ Q6. π(π₯) = { π₯+1 ππ π₯ < 2 ππ π₯ β₯ 2 ππ π₯ β€ 0 ππ π₯ > 0 4 ππ π₯ < β2 Q7. π(π₯) = {π₯ ππ β 2 β€ π₯ β€ 2 βπ₯ + 6 ππ π₯ > 2 2 Q8βQ10. Determine whether the equation defines π¦ as a function of π₯ Q8. 3π₯ β 5π¦ = 7 Q9. 2π₯ β 4π¦ 2 = 4 Q10. 2|π₯| + π¦ = 0 2 2.3 Getting information from the graph of a function Q1. The graph of a function β is given a) b) c) d) e) Find β(β2), β(0), β(2) and β(3) Find the domain and range of β Find the values of π₯ for which β(π₯) = 3 Find the values of π₯ for which β(π₯) β€ 3 Find the net change in h between π₯ = β3 and π₯ = 3 Q2. Graphs of the functions π and π are given. a) b) c) d) e) Which is larger, π(0) ππ π(0)? Which is larger, π(β3) or π(β3)? For which values of π₯ is π(π₯) = π(π₯)? Find the values of π₯ for which π(π₯) β€ π(π₯) Find the values of π₯ for which π(π₯) > π(π₯) 3 Q3βQ5. A function π is given. (π) sketch a graph of π (b) use the graph to find the domain and range of π Q3. π(π₯) = 2π₯ + 3 Q4. π(π₯) = π₯ β 2 β2 β€ π₯ β€ 5 Q5. π(π₯) = π₯ 2 β 1, β3 β€ π₯ β€ 3 Q6βQ7. The graph of the function π is given. Use the graph to estimate the following a) The domain and range of π b) The intervals on which π is increasing and on which π is decreasing. Q6. Q7. Q8. A function π is given. a) Graph the function b) Find the domain and range of π c) State approximately the intervals on which π is increasing and on which π is decreasing. d) Find all local maximum and local minimum values π(π₯) = π₯ 2 β 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. π(π₯) = 3π₯ β 2 3 π₯ = 2, π₯ = 3 Q2. β(π‘) = βπ‘ + 2 π‘ = β4, π‘ = 1 Q3. β(π‘) = 2π‘ 2 β π‘ π‘ = 3, π‘ = 6 Q4. π(π₯) = π₯ 3 β 4π₯ 2 1 Q5. π(π₯) = π₯ π₯ = 0, π₯ = 10 π₯ = 1, π₯ = π 5
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