# Evaluate the function at the indicated values

Math 3—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(𝑥) = 𝑥 2 − 6, Q2. 𝑓(𝑥) = 1−2𝑥 3 1 𝑓(−3), 𝑓(3), 𝑓(0), 𝑓 (2) 1 , 𝑓(2), 𝑓(−2), 𝑓 ( ) , 𝑓(𝑎), 𝑓(−𝑎), 𝑓(𝑎 − 1) 2 1 Q3. 𝑓(𝑥) = 𝑥 2 + 2𝑥, 𝑓(0), 𝑓(3), 𝑓(−3), 𝑓(𝑎), 𝑓(−𝑥), 𝑓 (𝑎) Q4—Q5. Evaluate the piecewise defined function at the indicated values. 𝑥2 Q4. 𝑓(𝑥) = { 𝑥+1 𝑖𝑓 𝑥 < 0 𝑖𝑓 𝑥 ≥ 0 𝑓(−2), 𝑓(−1), 𝑓(0), 𝑓(1), 𝑓(2) 𝑥 2 − 2𝑥 𝑖𝑓 𝑥 ≤ −1 Q5. 𝑓(𝑥) = { 𝑥 𝑖𝑓 − 1 < 𝑥 ≤ 1 −1 𝑖𝑓 𝑥 > 1 𝑓(−4), 3 𝑓 (− ) , 2 𝑓(−1), Q6—Q9. Find the domain of the function 1 Q6. 𝑓(𝑥) = 𝑥−3 Q7. 𝑓(𝑡) = √𝑡 + 1 Q8. 𝑔(𝑥) = √1 − 2𝑥 Q9. 𝑓(𝑥) = 3𝑥 1 𝑓(0), 𝑓(25) 2.2 Graphs of a function Q1—Q4. Sketch a graph of the function by first making a table of values. Q1. 𝑓(𝑥) = −𝑥 + 3, −3≤𝑥 ≤3 Q2. 𝑓(𝑥) = −𝑥 2 Q3. 𝑓(𝑥) = 1 + √𝑥 Q4. 𝑓(𝑥) = | 2𝑥| Q5—Q7. Sketch a graph of the piecewise defined function. 3 Q5. 𝑓(𝑥) = { 𝑥−1 𝑥 Q6. 𝑓(𝑥) = { 𝑥+1 𝑖𝑓 𝑥 < 2 𝑖𝑓 𝑥 ≥ 2 𝑖𝑓 𝑥 ≤ 0 𝑖𝑓 𝑥 > 0 4 𝑖𝑓 𝑥 < −2 Q7. 𝑓(𝑥) = {𝑥 𝑖𝑓 − 2 ≤ 𝑥 ≤ 2 −𝑥 + 6 𝑖𝑓 𝑥 > 2 2 Q8—Q10. Determine whether the equation defines 𝑦 as a function of 𝑥 Q8. 3𝑥 − 5𝑦 = 7 Q9. 2𝑥 − 4𝑦 2 = 4 Q10. 2|𝑥| + 𝑦 = 0 2 2.3 Getting information from the graph of a function Q1. The graph of a function ℎ is given a) b) c) d) e) Find ℎ(−2), ℎ(0), ℎ(2) and ℎ(3) Find the domain and range of ℎ Find the values of 𝑥 for which ℎ(𝑥) = 3 Find the values of 𝑥 for which ℎ(𝑥) ≤ 3 Find the net change in h between 𝑥 = −3 and 𝑥 = 3 Q2. Graphs of the functions 𝑓 and 𝑔 are given. a) b) c) d) e) Which is larger, 𝑓(0) 𝑜𝑟 𝑔(0)? Which is larger, 𝑓(−3) or 𝑔(−3)? For which values of 𝑥 is 𝑓(𝑥) = 𝑔(𝑥)? Find the values of 𝑥 for which 𝑓(𝑥) ≤ 𝑔(𝑥) Find the values of 𝑥 for which 𝑓(𝑥) > 𝑔(𝑥) 3 Q3—Q5. A function 𝑓 is given. (𝑎) sketch a graph of 𝑓 (b) use the graph to find the domain and range of 𝑓 Q3. 𝑓(𝑥) = 2𝑥 + 3 Q4. 𝑓(𝑥) = 𝑥 − 2 −2 ≤ 𝑥 ≤ 5 Q5. 𝑓(𝑥) = 𝑥 2 − 1, −3 ≤ 𝑥 ≤ 3 Q6—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(𝑥) = 𝑥 2 − 5𝑥 4 2.4 Average rate of change of a function Q1—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(𝑥) = 3𝑥 − 2 3 𝑥 = 2, 𝑥 = 3 Q2. ℎ(𝑡) = −𝑡 + 2 𝑡 = −4, 𝑡 = 1 Q3. ℎ(𝑡) = 2𝑡 2 − 𝑡 𝑡 = 3, 𝑡 = 6 Q4. 𝑓(𝑥) = 𝑥 3 − 4𝑥 2 1 Q5. 𝑔(𝑥) = 𝑥 𝑥 = 0, 𝑥 = 10 𝑥 = 1, 𝑥 = 𝑎 5
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