# Chapter 1 Study Guide

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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.

• 1.

### If , find C(3) and C(-2).

• A.

-2 and -8

• B.

-2 and 8

• C.

2 and 8

• D.

2 and -8

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?

• A.

D: [-3, 1] R: (- infinity, 5]

• B.

D: (- infinity, infinity), R: (- infinity, -1]

• C.

D: (- infinity, infinity), R: (- infinity, 5)

• D.

D: (- infinity, infinity), R: (- infinity, 5]

D. D: (- infinity, infinity), R: (- infinity, 5]
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

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

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

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

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

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

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

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