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5. Determine whether each table represents a linear function. For those that represent linear functions, write the function. For those that do not, explain why not.
a. x y
210 216
23 22
1 6
2 8
b. x y
23 28
22 26
0 1
1 2
6. A faucet leaks water at a constant rate. Tara places a measuring cup under the leak to catch the water. The table shows the number of milliliters of water in the cup at diff erent times.
Time (hours) Amount of Water (milliliters)
3.5 14
4 16
4.5 18
5 20
a. Determine the average rate of change for the problem situation. Be sure to include units.
b. Write a function to model the table of values.
c. Determine the amount of water in the cup after the faucet leaks at a constant rate for 12 hours.
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7. Gina has saved $420. She plans to spend $35 each month for music lessons. The function s(t) 5 235t 1 420 describes her savings, s, in dollars as a function of the time, t, in months.
a. Graph the function that describes Gina’s savings as a function of the time she works. Label the x{ and y{intercepts and explain what they mean in the problem situation.
b. Write the function you graphed in factored form.
c. Determine how much Gina will have left of her savings after 10 months.
8. Using the graph below, how many gallons of gas can be purchased for $15.80?
4
10
20
30
40
0 8 12 16Amount of Gasoline (gallons)
Cost
(dol
lars
)
x
y
9. Use the graph to determine when f(x) 5 5 and the value of f(5).
–4 –2 2
2
–2
–4
4
6
8
4 x
y
0–6–8
–6
–8
6 8
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11. Write the equation of a line that passes through the point (22, 6) and is parallel to the line that passes through the points (0, 24) and (3, 2).
12. Write the equation of a line that passes through the point (24, 25) and is perpendicular to a line that passes through the points (26, 8) and (10, 0).
13. Use the functions f(x) and g(x) to complete the comparison statements using <, >, or =.
x f(x)
23 20.5
22 0
21 0.5
0 1
–4 –2 2
2
–2
–4
4
6
8
4 x
y
0–6–8
–6
–8
6 8
a. f(23) g(23)
b. slope of f slope of g
c. y-intercept of f y-intercept of g
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14. Sara started with 12 comic books in her collection. She collected the same number of comic books each month until she had 20 comic books in the 4th month. Ashton started with 2 comic books in his collection and continues to collect 3 comic books each month.
0
Sara
x
y Ashton
Ashton started with 2 comic books in his collection and continues to collect 3 comic books each month.
a. Use what you know about Sara’s collection to determine the scale of each axis and interpret the origin on the graph.
b. Compare the slope and y-intercept for each function in terms of the quantities.
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