# Determine whether the given function is linear

Math 3βCollege Algebra Homework 2.5β2.8 Name: ______________________ Show all your work for full credit: 2.5 Linear Functions and Models Q1βQ3. Determine whether the given function is linear. If the function is linear, express the function in the form π(π₯) = ππ₯ + π Q1. π(π₯) = π₯(4 β π₯) Q2. π(π₯) = π₯+1 5 Q3. π(π₯) = (π₯ + 1)2 Q4βQ5. For the given linear function, make a table of values and sketch its graph. What is the slope of the graph? Q4. π(π₯) = 2π₯ β 5 2 Q5. π(π‘) = β π‘ + 2 3 Q6βQ7. A linear function is given. A) sketch the graph the rate of change of the function. b) Find the slope of the graph. C) Find Q6. π(π₯) = 2π₯ β 6 Q7. π£(π‘) = β 10 3 π‘ β 20 Q8. The amount of trash in a country landfill is modeled by the function π(π₯) = 150π₯ + 32,000 Where π₯ is the number of years since 1996 and π(π₯) is measured in thousands of tons. a) Sketch the graph of T b) What is the slope of the graph? c) At what rate is the amount of trash in the landfill increasing per year? 1 2.6 Transformations of functions Q1βQ4. Explain how the graph of g is obtained from the graph of π. Q1. π(π₯) = π₯ 2 π(π₯) = (π₯ + 2)2 Q2. π(π₯) = π₯ 2 π(π₯) = π₯ 2 + 2 Q3. π(π₯) = |π₯| π(π₯) = |π₯ + 2| β 2 Q4. π(π₯) = |π₯| π(π₯) = |π₯ β 2| + 2 Q5. Use the graph of π¦ = π₯ 2 to graph the follow. a) b) c) d) π(π₯) = π₯ 2 + 1 π(π₯) = (π₯ β 1)2 π(π₯) = βπ₯ 2 π(π₯) = (π₯ β 1)2 + 3 Q6βQ9. Sketch the graph of the function using transformations. Q6. π(π₯) = |π₯| β 1 1 Q8. π(π₯) = 3 β (π₯ β 1)2 2 1 Q7. π(π₯) = 4 π₯ 2 1 Q9. π(π₯) = βπ₯ + 4 β 3 2 Q10βQ11. A function π is given, write an equation for the final transformed graph. Q10. π(π₯) = |π₯|, shift 2 units to the left and shift downward 5 units. 4 Q11. π(π₯) = βπ₯; reflect in the y-axis and shift upward 1 unit. Q12βQ13. Determine whether the function π is even, odd, or neither. If π is even or odd, use symmetry to sketch the graph. Q12. π(π₯) = π₯ 4 Q13. π(π₯) = π₯ 2 + π₯ 2 2.7 Combining Functions Q1βQ4. Find π + π, π β π, ππ, πππ π/π and their domain Q1. π(π₯) = π₯ 2 + π₯, π(π₯) = π₯ 2 Q2. π(π₯) = 5 β π₯, π(π₯) = π₯ 2 β 3π₯ Q3. π(π₯) = β25 β π₯ 2 , π(π₯) = βπ₯ + 3 2 Q4. π(π₯) = π₯ , 4 π(π₯) = π₯+4 Q5βQ7. Use π(π₯) = 2π₯ β 3 and π(π₯) = 4 β π₯ 2 to evaluate the expression. Q5. A) π(π(0)) B) π(π(0)) Q6. π΄) (πΒ°π)(β2) B) (πΒ°π)(β2) Q7. π΄) (πΒ°π)(π₯) B) (πΒ°π)(π₯) Q8—Q9. Find the functions πΒ°π, πΒ°π, πΒ°π, and πΒ°π and their domains. Q8. π(π₯) = 1 π₯ Q9. π(π₯) = π₯ 2 π(π₯) = 2π₯ + 4 π(π₯) = π₯ + 1 3 2.8 One to One Functions and their Inverses Q1—Q3. Determine whether the function is one-to-one. Q1. π(π₯) = β2π₯ + 4 Q2. β(π₯) = π₯ 2 β 2π₯ Q3. π(π₯) = βπ₯ Q4—Q6. Assume that π is a one-to-one function. Q4. if π(2) = 7, find π β1 (7). Q5. ππ π β1 (3) = β1, find π(β1) Q6. If π(π₯) = 5 β 2π₯, find π β1 (3) Q7βQ10. Use the inverse Function property to show that π πππ π are inverse of each other. Q7. π(π₯) = π₯ β 6 π(π₯) = π₯ + 6 Q8. π(π₯) = 3π₯ + 4 π(π₯) = Q9. π(π₯) = π₯ 2 β 9, π₯ β₯ 0, π₯+2 Q10. π(π₯) = π₯β2 π₯β4 3 π(π₯) = βπ₯ + 9, π₯ β₯ β9 π(π₯) = 2π₯+2 π₯β1 Q11βQ13 Find the inverse function of π. Q11. π(π₯) = 3π₯ + 5 Q12. π(π₯) = 2π₯+5 π₯β7 Q13. π(π₯) = 4 β π₯ 2 , π₯ β₯ 0 Q14βQ15. A function π is given. A) sketch the graph of π B) use the graph of π to sketch the graph of π β1 C) Find π β1 Q14. π(π₯) = 3π₯ β 6 Q15. π(π₯) = βπ₯ + 1 4
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