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MAT 150 - Functions, Graphs & Models: Linear Functions This study guide is 10 questions graded on correctness. You make take the quiz as many times as you like and I will assign you the highest score. Your scores will go to your email acount so make sure you save this for your records.
Questions and Answers
1.
If , find C(3) and C(-2).
A.
-2 and -8
B.
-2 and 8
C.
2 and 8
D.
2 and -8
Correct Answer B. -2 and 8
Explanation The given answer is correct because C(3) and C(-2) are represented by the values -2 and 8 respectively. The pattern is that the value of C(x) is equal to the square of x minus 4. Therefore, C(3) = 3^2 - 4 = 9 - 4 = 5, and C(-2) = (-2)^2 - 4 = 4 - 4 = 0.
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2.
Graph on your graphing calculator. What is the domain and range?
Explanation The correct answer is D: (- infinity, infinity), R: (- infinity, 5]. The domain is (- infinity, infinity) because there are no restrictions on the x-values of the graph. The range is (- infinity, 5] because the y-values of the graph can be any number less than or equal to 5, but it cannot be greater than 5.
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3.
Find the slope of the line through (-4, 6) ad (8, -16).
A.
-11/6
B.
-6/11
C.
5/6
D.
6/5
Correct Answer A. -11/6
Explanation To find the slope of a line, we can use the formula: slope = (y2 - y1) / (x2 - x1). In this case, the coordinates (-4, 6) and (8, -16) represent the points (x1, y1) and (x2, y2) respectively. Plugging these values into the formula, we get: slope = (-16 - 6) / (8 - (-4)) = -22 / 12 = -11 / 6. Therefore, the correct answer is -11/6.
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4.
Find the slope of 2x - 3y = 7.
A.
-2/3
B.
-2
C.
2/3
D.
2
Correct Answer C. 2/3
Explanation To find the slope of a linear equation in the form of y = mx + b, we need to rearrange the given equation into this form. Starting with 2x - 3y = 7, we can isolate y by subtracting 2x from both sides, resulting in -3y = -2x + 7. Dividing both sides by -3, we get y = (2/3)x - 7/3. Comparing this equation to y = mx + b, we can see that the slope is 2/3. Therefore, the correct answer is 2/3.
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5.
Write the equation of a line that has slope 4 and y-intercept 6.
A.
Y = 6x + 4
B.
Y = 4x + 6
C.
4x + 6y = 10
D.
Y = 4x - 6
Correct Answer B. Y = 4x + 6
Explanation The equation of a line is typically written in the form y = mx + b, where m represents the slope and b represents the y-intercept. In this case, the slope is given as 4 and the y-intercept is given as 6. Therefore, the equation of the line can be written as y = 4x + 6.
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6.
Write the equation of the line that has slope and passes through (4, -6).
A.
Y = -3/4 x - 3
B.
Y = -3/4 x - 10
C.
Y = -3/4 x + 9
D.
Y = -3/4 x - 1/2
Correct Answer A. Y = -3/4 x - 3
Explanation The equation of a line can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept. In this case, the slope is -3/4. We are also given that the line passes through the point (4, -6). Plugging these values into the equation, we get -6 = (-3/4)(4) + b. Simplifying, we find that b = -3. Therefore, the equation of the line is y = -3/4 x - 3.
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7.
Write the equation of the line that passes through (-8, 3) and is perpendicular to the line 4x + 3y = 6.
A.
Y = -4/3 x - 23/3
B.
Y = -3/4 x - 3
C.
Y = 3/4 x + 3
D.
Y = 3/4 x + 9
Correct Answer D. Y = 3/4 x + 9
Explanation To find the equation of a line that is perpendicular to another line, we need to find the negative reciprocal of the slope of the given line. The given line has a slope of -4/3, so the perpendicular line will have a slope of 3/4. We can then use the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is the given point (-8, 3) and m is the slope. Plugging in the values, we get y - 3 = 3/4(x - (-8)). Simplifying, we get y - 3 = 3/4(x + 8), which can be rearranged to y = 3/4x + 9. Therefore, the correct answer is y = 3/4x + 9.
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8.
Teacher Salaries The average salary of a classroom teacher in the United States is given by f(x) = 982.06x + 32903.77, where x is the number of years after 1990. What is the average salary in 2005 according to this equation?
A.
$48,616.73
B.
$2001934.07
C.
$47,634.67
D.
$37814.07
Correct Answer C. $47,634.67
Explanation The average salary in 2005 according to the equation f(x) = 982.06x + 32903.77 can be found by substituting x = 2005 - 1990 = 15 into the equation. This gives f(15) = 982.06(15) + 32903.77 = 14730.9 + 32903.77 = 47634.67. Therefore, the average salary in 2005 according to this equation is $47,634.67.
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9.
Phone Bills For interstate calls, AT&T charges 10 cents per minute plus a base charge of $2.99 each month. Write an equation for the monthly charge y as a funtion of the number of minutes of use.
A.
Y = 10x + 2.99
B.
Y = 2.99x + .10
C.
Y = .10x + 2.99
D.
Y = 2.99x + .10x
Correct Answer C. Y = .10x + 2.99
Explanation The correct equation for the monthly charge y as a function of the number of minutes of use is y = 10x + 2.99. This equation represents the base charge of $2.99 each month plus the additional charge of 10 cents per minute for interstate calls.
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10.
Go to pg 80 and do #29 b and c.
A.
B. f(25000) = 448.11. $448.11 is the payment to borrow $25,000.
C. A = 20,000
B.
B. f(25000) = 448.11. $448.11 is the monthly payment to borrow $25,000.
C. A = 20,000
C.
B. f(25000) = 448.11. $448.11 is the monthly payment to borrow $25,000.
C. A = 15,000
D.
B. f(25000) = 537.73. $537.73 is the monthly payment to borrow $25,000.
C. A = 20,000
Correct Answer B. B. f(25000) = 448.11. $448.11 is the monthly payment to borrow $25,000.
C. A = 20,000