Chapter 1 Quiz: Linear Functions

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Chapter 1 Quiz: Linear Functions - Quiz

It is no lie that mathematics is one of the most disliked topics by students today. People tend to fear algebra and calculus even before they start learning on them. Have you been having some problems when it comes to solving linear equations? The quiz below is designed to help you polish out your skills as it gives you some practice activities on functions, graphs and models. Give it a shot!


Questions and Answers
  • 1. 

    Given , find C(2) and C(-4).

    • A.

      0 and -24

    • B.

      16 and 40

    • C.

      0 and 40

    • D.

      -16 and -24

    Correct Answer
    A. 0 and -24
    Explanation
    The question is asking for the values of C(2) and C(-4). The given answer is 0 and -24. Since we are not provided with any information or context about what C represents, it is not possible to determine the exact calculations or reasoning behind the answer. Therefore, an explanation cannot be provided.

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  • 2. 

    Graph   on your graphing calculator and then give the domain and range.

    • A.

      D: [-2, 2] R: (-infinity, 6]

    • B.

      D: (-infinity, infinity) R: (-infinity, 6]

    • C.

      D: (-infinity, infinity) R: [6, infinity)

    • D.

      D: (-infinity, infinity) R: (-infinity, 6)

    Correct Answer
    B. D: (-infinity, infinity) R: (-infinity, 6]
    Explanation
    The correct answer is D because when you graph a function on a graphing calculator, the domain is typically the set of all real numbers (represented by (-infinity, infinity)) and the range is the set of all possible y-values that the function can take on. In this case, the range is (-infinity, 6] because the y-values can go as low as negative infinity but can only reach up to 6.

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  • 3. 

    Find the slope through the points (4, -2) and (-1, 6).

    • A.

      -5/8

    • B.

      8/5

    • C.

      -8/5

    • D.

      -3

    Correct Answer
    C. -8/5
    Explanation
    The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula (y2 - y1) / (x2 - x1). In this case, the points are (4, -2) and (-1, 6). Plugging the values into the formula, we get (6 - (-2)) / (-1 - 4) = 8 / -5 = -8/5. Therefore, the slope of the line passing through these points is -8/5.

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  • 4. 

    Find the slope of the linear equation: 

    • A.

      2

    • B.

      -1/2

    • C.

      -6

    • D.

      -2

    Correct Answer
    D. -2
    Explanation
    The slope of a linear equation is the coefficient of the variable x. In this case, the given equation does not have a variable x, so the slope is 0. However, the answer given is -2, which is incorrect.

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  • 5. 

    Write the equation of the line given slope of 5 and y-intercept of -2.

    • A.

      Y = 5x - 2

    • B.

      Y = -2x + 5

    • C.

      Y = 5x + 2

    • D.

      5x - 2y = 3

    Correct Answer
    A. Y = 5x - 2
    Explanation
    The equation of a line can be written in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the given slope is 5 and the y-intercept is -2. Plugging these values into the equation form, we get y = 5x - 2.

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  • 6. 

    Write the equation of a line with slope  and through the point (9, -3).

    • A.

      Y = 2/3 x - 6

    • B.

      Y = 2/3 x - 9

    • C.

      Y = 2/3 x - 3

    • D.

      Y = 2/3 x + 3

    Correct Answer
    B. Y = 2/3 x - 9
    Explanation
    The equation of a line is typically written in the form y = mx + b, where m represents the slope of the line and b represents the y-intercept. In this case, the slope is given as 2/3. Since the line passes through the point (9, -3), we can substitute these values into the equation. By substituting x = 9 and y = -3 into the equation y = 2/3 x + b, we can solve for b. This gives us -3 = 2/3 * 9 + b, which simplifies to -3 = 6 + b. Solving for b, we find that b = -9. Therefore, the equation of the line is y = 2/3 x - 9.

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  • 7. 

    Write the equation of the line through the point (-1, 5) and perpendicular to the line 4x + y = 6.

    • A.

      Y = 1/4 x + 6

    • B.

      Y = -4x + 1

    • C.

      Y = 1/4 x + 21/4

    • D.

      Y = -1/4 x + 19/4

    Correct Answer
    C. Y = 1/4 x + 21/4
    Explanation
    The equation of a line perpendicular to another line can be found by taking the negative reciprocal of the slope of the given line. The given line has a slope of -4x + 1, so the perpendicular line will have a slope of 1/4. Since the line passes through the point (-1, 5), we can use the point-slope form of a line to find the equation. Plugging in the values, we get y - 5 = 1/4(x - (-1)), which simplifies to y - 5 = 1/4(x + 1). Rearranging the equation, we get y = 1/4x + 1/4 + 5, which simplifies to y = 1/4x + 21/4. Therefore, the correct answer is y = 1/4x + 21/4.

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  • 8. 

    Personal Savings  Using data from 1960 to 2009, th personal savings rate (as a percent of disposable income) of Americans can be modeled by the function  where x is the number of years after 1960.  Use the model to estimate the personal savings rate in 2013 to the nearest tenth.

    • A.

      574%

    • B.

      3670265.7%

    • C.

      5.2%

    • D.

      5.7%

    Correct Answer
    D. 5.7%
    Explanation
    The correct answer is 5.7%. The question states that the personal savings rate of Americans can be modeled by a function using data from 1960 to 2009. The function is not provided, but it can be used to estimate the personal savings rate in 2013. Therefore, the estimated personal savings rate in 2013 is 5.7% to the nearest tenth.

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  • 9. 

    Cable Bill  A cable complany charges and flat monthly fee of $95 for basic channels and an additional $7 for each premium channel.  Write an equation to model the cable company's monthly fees.

    • A.

      Y = 7x + 95

    • B.

      Y = 95x + 7

    • C.

      Y = 102x

    • D.

      Y = 7x

    Correct Answer
    A. Y = 7x + 95
    Explanation
    The correct equation to model the cable company's monthly fees is y = 7x + 95. This equation represents the flat monthly fee of $95 for basic channels (represented by the constant term 95) and an additional $7 for each premium channel (represented by the coefficient of x, which represents the number of premium channels). By multiplying the number of premium channels by 7 and adding it to the flat fee, we can determine the total monthly fee.

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  • 10. 

    Blood Alcohol Percent  Using the table on pg 72 #49, what does f(4) equal?  Tell what this represents in this situation.

    • A.

      F(4) = 0.18; With 4 drinks there is a blood alcohol percent of 0.18.

    • B.

      F(4) = 0.18; When a 100 pound woman has 4 alcoholic beverages, she has a blood alcohol percent of 0.18.

    • C.

      F(4) = 0.18; With 4 alcoholic drinks a person will have a blood alcohol percent of 0.18.

    • D.

      F(4) = 0.18; The average rate of change in blood alcohol percent is 0.18 for a 100 pound woman who has 4 alcoholic drinks.

    Correct Answer
    B. F(4) = 0.18; When a 100 pound woman has 4 alcoholic beverages, she has a blood alcohol percent of 0.18.
    Explanation
    The correct answer is "f(4) = 0.18; When a 100 pound woman has 4 alcoholic beverages, she has a blood alcohol percent of 0.18." This answer accurately represents the situation described in the question, which is finding the blood alcohol percent for a 100 pound woman who has consumed 4 alcoholic beverages. The answer provides the specific values and units that correspond to the given situation.

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