MATH 3 SDSU Equations & Domain of The Function Exercises

Math 3—College Algebra2.1—2.4 Homework
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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