Answer the questions below ⦁ 1. A car's speed increases as it merges onto a highway. The car travels at 65 mph on the highway until it slows to exit. The car then stops at three traffic lights before reaching its destination. Draw a sketch of a graph that shows the car's speed over time.
⦁ 2. For the table, identify the independent and dependent variables. Explain the relationship using words, and an equation (equation example: C = 2s + 20).
3. Number of Snacks Purchased, “s” Total Cost, “C”
0 $18
1 $21
2 $24
3 $27
⦁ 4. Graph the function shown on this table. Tell whether the function is linear or nonlinear.
x y
1 0
2 1
3 8
4 20
⦁ 5. A truck originally held 24 chairs. You remove 2 chairs at a time. The number of chairs n remaining after you make t trips is represented by n = 24 − 2t. Will this be a continuous or discreet graph? Why?
⦁ 6. Write a function rule to represent the situation: Your total cost C for hiring a garden designer is $200 for an initial consultation plus $45 for each hour h the designer spends drawing plans.
⦁ 7. Is this relation a function {(−1, 7), (9, 4), (3, −2), (5, 3), (9, 1)}? Why or why not?
⦁ 8. Evaluate the function for x = 2, then evaluate the function for x = 7.
h(x) = −4x + 61 (SHOW YOUR WORK)
⦁ 9. Find the next two terms of the difference.
−2,−5,−8,−11,…
⦁ 10. Tell whether the sequence is arithmetic. If it is, identify the common difference.
−15,−5,5,15,…
1. The graph would show an increasing slope as the car merges onto the highway, maintains a constant speed on the highway, slows down as it exits, stops at traffic lights (flat line), and then reaches its destination.
2. Independent variable: Number of Snacks Purchased (s)
Dependent variable: Total Cost (C)
Relationship: The total cost increases by $3 for each additional snack purchased. Equation: C = 3s + 18
4. The function is nonlinear, as the values are not increasing at a constant rate.
5. It will be a discrete graph because the number of chairs can only decrease by 2 at a time, leading to specific and distinct points on the graph.
6. C(h) = 200 + 45h
7. No, this relation is not a function because the x-value 9 is associated with two different y-values (4 and 1).
8. h(2) = -4(2) + 61 = 53
h(7) = -4(7) + 61 = 33
9. The next two terms of the difference are -14, -17.
10. The sequence is arithmetic with a common difference of 10.