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Coordinate Algebra Practice EOCT Answers Unit 3 #1 Two lines are graphed on this coordinate plane. Which point appears to be a solution of the equations of both lines? A. (0, –2) B. (0, 4) C. (2, 0) D. (3, 1) Unit 3 #2 Based on the tables, at what point do the lines y = –x + 5 and y = 2x – 1 intersect? A. (1, 1) B. (3, 5) C. (2, 3) D. (3, 2) Unit 3 #3 The first term in this sequence is –1. Unit 3 Which function represents the sequence? A. an = an-1 + 1 B. an = an-1 + 2 C. an = 2an-1 – 1 D. an = 2an-1 – 3 Strategy: Use table to substitute n into each equation. Then, simplify and determine whether the result is the value of an in the table. #3 Which function represents the sequence? Note: a1 = –1 A. an = an-1 + 1 a2 = a2-1 + 1 = a1 + 1 = –1 + 1 = 0 Unit 3 First, test Equation A Equation A is not answer, since a2 1 #3 Which function represents the sequence? Note: a1 = –1 A. an = an-1 + 1 a2 = a2-1 + 1 = a1 + 1 = –1 + 1 = 0 Unit 3 First, test Equation A Equation A is not answer, since a2 1 #3 Which function represents the sequence? Unit 3 Note: a1 = –1 Next, test Equation B B. an = an-1 + 2 Answer: B a2 = a2-1 + 2 = a1 + 2 = –1 + 2 = 1 a3 = a3-1 + 2 = a2 + 2 = 1 + 2 = 3 a4 = a4-1 + 2 = a3 + 2 = 3 + 2 = 5 a5 = a5-1 + 2 = a4 + 2 = 5 + 2 = 7 YES YES YES YES #4 Which function is modeled in this table? Unit 3 A. f(x) = x + 7 B. f(x) = x + 9 C. f(x) = 2x + 5 D. f(x) = 3x + 5 Strategy: Use table to substitute x into each equation. Then, simplify and determine whether the result is the value of f(x) in the table. #4 Which function is modeled in this table? Unit 3 A. f(x) = x + 7 ? YES ? NO B. f(x) = x + 9 C. f(x) = 2x + 5 D. f(x) = 3x + 5 A. f(x) = x + 7 f(1) = 1 + 7 = 8 f(2) = 2 + 7 = 9 First, test Equation A YES NO #4 Which function is modeled in this table? Unit 3 A. f(x) = x + 7 B. f(x) = x + 9 ? NO C. f(x) = 2x + 5 D. f(x) = 3x + 5 Next, test Equation B B. f(x) = x + 9 f(1) = 1 + 9 = 10 NO Next, test Equation C C. f(x) = 2x + 5 f(1) = 2(1) + 5 = 2 + 5=7 NO #4 Which function is modeled in this table? Unit 3 A. f(x) = x + 7 B. f(x) = x + 9 C. f(x) = 2x + 5 D. f(x) = 3x + 5 Next, test Equation D C. f(x) = 3x + 5 f(1) = 3(1)+5 = 3+5 = 8 YES f(2) = 3(2)+5 = 6+5 = 11 YES ? YES ? YES ? YES ? YES f(3) = 3(3)+5 YES = 9+5 = 14 f(4) = 3(4)+5 YES = 12+5 = 17 #5 Which explicit formula describes the pattern in this table? Unit 3 A. d = 3.14 × C B. 3.14 × C = d C. 31.4 × 10 = C D. C = 3.14 × d Strategy: Use values in table to substitute d and C into each equation. Then, simplify and determine whether both sides of the equation are equal. #5 Which explicit formula describes the pattern in this table? Unit 3 A. d = 3.14 × C B. 3.14 × C = d C. 31.4 × 10 = C D. C = 3.14 × d Test answer A A. d = 3.14 × C 2 = 3.14 × 6.28 2 19.72 NO Test answer B B. 3.14 × C = d 3.14 × 6.28 = 2 19.72 2 NO #5 Which explicit formula describes the pattern in this table? Unit 3 A. d = 3.14 × C B. 3.14 × C = d C. 31.4 × 10 = C D. C = 3.14 × d Test answer C C. 31.4 × 10 = C 31.4 × 10 = 6.28 314 6.28 NO Test answer D D. C = 3.14 × d 6.28 = 3.14 × 2 6.28 6.28 YES #6 If f(12) = 4(12) – 20, which function gives f(x)? A. f(x) = 4x B. f(x) = 12x C. f(x) = 4x – 20 D. f(x) = 12x – 20 Unit 3 #7 A farmer owns a horse that can continuously run an average of 8 miles an hour for up to 6 hours. Let y be the distance the horse can travel for a given x amount of time in hours. The horse’s progress can be modeled by a function. Which of the following describes the domain of the function? A. 0 ≤ x ≤ 6 B. 0 ≤ y ≤ 6 C. 0 ≤ x ≤ 48 D. 0 ≤ y ≤ 48 Unit 3 #8 A population of squirrels doubles every year. Initially Unit 3 there were 5 squirrels. A biologist studying the squirrels created a function to model their population growth, P(t) = 5(2t) where t is time. The graph of the function is shown. What is the range of the function? A. any real number B. any whole number greater than 0 C. any whole number greater than 5 D. any whole number greater than or equal to 5 #9 The function graphed on this coordinate grid Unit 3 shows f(x), the height of a dropped ball in feet after its xth bounce. On which bounce was the height of the ball 10 feet? A. bounce 1 B. bounce 2 C. bounce 3 D. bounce 4 Unit 3 #10 To rent a canoe, the cost is $3 for the oars and life preserver, plus $5 an hour for the canoe. Which graph models the cost of renting a canoe? Formula to model cost of renting canoe x: # of hours rented C: Total rental cost C(x) = 5x + 3 The graph should be a line with a slope of 5 and y-intercept of 3. Unit 3 #10 To rent a canoe, the cost is $3 for the oars and life preserver, plus $5 an hour for the canoe. Which graph models the cost of renting a canoe? Cost Formula: C(x) = 5x + 3 A. Answer A is incorrect. First, the graph is not linear. The graph has a y-intercept = 0, but the Cost Formula has a y-intercept = 3. Unit 3 #10 To rent a canoe, the cost is $3 for the oars and life preserver, plus $5 an hour for the canoe. Which graph models the cost of renting a canoe? Cost Formula: C(x) = 5x + 3 D. The graph is a Horizontal Line. y=5 Answer D is incorrect. The equation y = 5 concludes that the total rental cost will be $5, regardless of the number of hours rental. (i.e. The canoe rental cost would be $5, if rented for 1 hour or 20 hours.) To rent a canoe, the cost is $3 for the oars and life preserver, plus $5 an hour for the canoe. Which graph models the cost of renting a canoe? Unit 3 #10 Cost Formula: C(x) = 5x + 3 B. Answer B is incorrect. The graph has a y-intercept = 5, but the Cost Formula has a y-intercept = 3. Unit 3 #10 To rent a canoe, the cost is $3 for the oars and life preserver, plus $5 an hour for the canoe. Which graph models the cost of renting a canoe? Cost Formula: C(x) = 5x + 3 C. Answer C is correct. The graph and Cost Formula have a y-intercept = 3. #11 Juan and Patti decided to see who could read Unit 3 the most books in a month. They began to keep track after Patti had already read 5 books that month. This graph shows the number of books Patti read for the next 10 days. If Juan has read no books before the fourth day of the month and he reads at the same rate as Patti, how many books will he have read by day 12? Step 1: Determine the time that passes for Juan to read from day 4 to day 12 (12–4 = 8 days) 8 days #11 Juan and Patti decided to see who could read the most Unit 3 books in a month. They began to keep track after Patti had already read 5 books that month. This graph shows the number of books Patti read for the next 10 days. If Juan has read no books before the fourth day of the month and he reads at the same rate as Patti, how many books will he have read by day 12? 10 8 8 days Step 2: Calculate the rate of books to days for Patti in 8 days. Thus, the number of books Patti read in 8 days was 10 books. Step 3: If Juan read at the same rate as Patti, then by day 12 he would have also read 10 books. #12 Which function represents this sequence? 3 A. f(n) = 3n-1 B. f(n) = 6 n-1 C. f(n) = 3(6 n-1) D. f(n) = 6(3 n-1) 3 3 Unit 3 3 Use geometric sequence formula an = a1 rn–1 First Term: a1 = 6 Common Ratio: r = 3 an = 6(3n–1) #13 The first term in this sequence is 3. Which function represents the sequence? +7 Unit 3 +7 +7 +7 Use arithmetic sequence formula A. f(n) = n + 3 an = a1 + d(n – 1) B. f(n) = 7n – 4 First Term: a1 = 3 Common Difference: d = 7 C. f(n) = 3n + 7 D. f(n) = n + 7 an = 3 + 7(n – 1) = 3 + 7n – 7 = 7n – 4 Unit 3 #14 The points (0, 1), (1, 5), (2, 25), (3, 125) are on the graph of a function. Which equation represents that function? Strategy: Test one or more of the A. f(x) = 2x points in each equation to see if both coordinates work. B. f(x) = 3x C. f(x) = 4x D. f(x) = 5x Try the point (1,5) Substitute 1 for x. If the answer is 5, then the equation works. A. f(1) = 21 = 2 B. f(1) = 31 = 3 C. f(1) = 41 = 4 D. f(1) = 51 = 5 #15 A function g is an odd function. If g(–3) = 4, which other point lies on the graph of g? A. (3, –4) B. (–3, –4) C. (4, –3) D. (–4, 3) Note: g(–3)=4 rewritten as a point is (–3,4) Odd Function Rule (x,y) (–x, –y) Answer (–3,4) (3, –4) Unit 3 #16 Which statement is true about the function f (x) = 7? Unit 3 A. The function is odd because –f(x) = f(–x). B. The function is even because –f(x) = f(–x). Odd function rule C. The function is odd because f(x) = f(–x). D. The function is even because f(x) = f(–x). Note: f (x) = 7 is the equation of a horizontal line. It can be rewritten as y = 7. Every horizontal line is an even function. #17 A. C. Which scatter plot BEST represents a model of linear growth? Exponential Growth Linear Negative Correlation B. Linear Growth D. No Correlation Unit 3 #18 Which scatter plot BEST represents a model of exponential growth? A. C. Unit 3 B. Exponential Growth Linear Growth D. Linear Decay Negative Correlation Weak Linear Growth Which table represents an exponential function? #19 A. B. C. D. Unit 3 If the parent function is f(x) = mx + b, what Unit 3 is the value of the parameter m for the line passing through the points (–2, 7) and (4, 3)? #20 A. –9 B. 3 2 C. –2 D. 2 3 m represents the slope of a line Formula for the slope m of a line passing through the points (x1,y1) and (x2,y2) m y1 y 2 x1 x 2 OR m y 2 y1 x 2 x1 Slope m of line passing through points (–2,7) and (4,3) m 73 2 4 = 4 6 2 3