Linear Equations and Functions Quiz
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Linear Equations and Functions Quiz

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@GentlestHyena

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Questions and Answers

What is the slope of the line represented by the equation y = 7x + 4?

  • 4
  • 0
  • 1
  • 7 (correct)

    • What can be said about two lines that are parallel in the xy-plane?

  • They intersect at a right angle.
  • They always intersect at some point.
  • They have different slopes.
  • They have the same slope. (correct)

    • If the line is parallel to y = 7x + 4 and passes through (0, 5), what is the y-intercept of this new line?

  • 5 (correct)
  • 7
  • 4
  • 0

    • What is the equation of the line that passes through (0, 5) and is parallel to y = 7x + 4?

    <p>y = 7x + 5</p> Signup and view all the answers

    Which form can be used to express the equation of the line passing through (0, 5) and having a slope of 7?

    <p>Slope-intercept form</p> Signup and view all the answers

    What is the function that represents the maximum amount that the electrician charges?

    <p>h(x) = −41</p> Signup and view all the answers

    If the electrician charges an hourly rate represented by h(x) = −x + 41, how does the charge change with respect to x?

    <p>The charge decreases linearly with x.</p> Signup and view all the answers

    What is the perimeter of square Y if it is twice the perimeter of square X, which has a side length of 12 cm?

    <p>48 cm</p> Signup and view all the answers

    What is the length of one side of square Y if its perimeter is 96 cm?

    <p>24 cm</p> Signup and view all the answers

    Which equation correctly describes the charge structure of the electrician’s one-time fee based on the given options?

    <p>h(x) = −x + 41</p> Signup and view all the answers

    What does the slope of the graph represent in the context of the electrician's charges?

    <p>The hourly rate the electrician charges</p> Signup and view all the answers

    If h(0) = 41, what does this point signify about the electrician's charges?

    <p>The one-time fee is $41</p> Signup and view all the answers

    Which of the following equations accurately defines the function h?

    <p>h(x) = 41 - x</p> Signup and view all the answers

    What value represents the total charge after one hour of work according to h?

    <p>$40</p> Signup and view all the answers

    In the equation y = 5x + 7, what does the number 7 represent?

    <p>The one-time fee charged for the service</p> Signup and view all the answers

    For the function h, what would be the expected charge if 3 hours of work are performed?

    <p>$38</p> Signup and view all the answers

    Which equation corresponds to an increase in the hourly rate charged by the electrician?

    <p>y = 7x</p> Signup and view all the answers

    What is the total charge if the electrician worked for 0 hours given any of the provided equations?

    <p>$41</p> Signup and view all the answers

    What is the value of f(2) for the function defined as f(x) equals 201% of x?

    <p>402</p> Signup and view all the answers

    Which of the following represents the point where the function f intersects the x-axis?

    <p>(-14, 0)</p> Signup and view all the answers

    What form does the function f(x) take based on the given definition?

    <p>Linear</p> Signup and view all the answers

    At what value of x does the function f(x) reach 201?

    <p>100</p> Signup and view all the answers

    What is the output of the function f when x = 0?

    <p>0</p> Signup and view all the answers

    Which of the following values does f(3) equal?

    <p>6.03</p> Signup and view all the answers

    What does the output of f(x) indicate when x is greater than 14?

    <p>The output increases.</p> Signup and view all the answers

    Which of these points represents f(x) when x is negative?

    <p>(−14, 0)</p> Signup and view all the answers

    What is the expression for f(0) using the function defined as f(x) = (x − 6)(x − 2)(x + 6)?

    <p>-72</p> Signup and view all the answers

    How does the graph of g(x) relate to f(x) if g(x) is obtained by translating f(x) up by 4 units?

    <p>g(x) = f(x) + 4</p> Signup and view all the answers

    What is g(0) if g(x) is defined as the translation of f(x) = (x − 6)(x − 2)(x + 6) up 4 units?

    <p>72</p> Signup and view all the answers

    What is the product of the roots of the equation f(x) = 0 when f(x) = (x - 6)(x - 2)(x + 6)?

    <p>72</p> Signup and view all the answers

    Which of the following is true about the function f(x)?

    <p>It has three real roots.</p> Signup and view all the answers

    What's the leading coefficient of the polynomial given by f(x) = (x − 6)(x − 2)(x + 6)?

    <p>1</p> Signup and view all the answers

    What does the term 'translation' refer to in the context of graph transformations?

    <p>Shifting the graph up, down, left, or right.</p> Signup and view all the answers

    If the graph of f(x) is translated down 3 units, what is the new function represented?

    <p>g(x) = f(x) - 3</p> Signup and view all the answers

    Study Notes

    Linear Equations

    • Find the equation of a line that passes through the point (0, 5) and is parallel to the line y = 7x + 4
    • Parallel lines have the same slope
    • The slope of y = 7x + 4 is 7
    • The equation of the line that passes through (0, 5) and has a slope of 7 is y = 7x + 5

    Interpreting Linear Functions

    • The graph of an electrician’s charges is a straight line, indicating a one-time fee plus an hourly rate
    • The slope of the graph represents the electrician's hourly rate
    • The y-intercept of the graph represents the electrician's one-time fee

    Square Perimeters

    • Square X has a side length of 12 centimeters
    • The perimeter of square X is 12 * 4 = 48 centimeters
    • The perimeter of square Y is 2 * 48 = 96 centimeters
    • One side of square Y has a length of 96 / 4 = 24 centimeters

    Linear Functions and Evaluating

    • The function h(x) satisfies h(0) = 41 and h(1) = 40
    • The slope of the line representing h(x) is (40 - 41) / (1 - 0) = -1
    • The equation of h(x) is h(x) = -x + 41

    Solving Quadratic Equations

    • Solve the quadratic equation (x - 2)^2 = 3x + 34
    • Expand the left side of the equation: x^2 - 4x + 4 = 3x + 34
    • Move all terms to one side: x^2 - 7x - 30 = 0
    • Factor the quadratic equation: (x - 10)(x + 3) = 0
    • The solutions are x = 10 and x = -3
    • Since x > 0, the solution is x = 10

    Function Definitions and Translations

    • The function f(x) is defined as f(x) = (x - 6)(x - 2)(x + 6)
    • The graph of y = g(x) is obtained by translating the graph of y = f(x) up 4 units
    • Therefore, g(x) = f(x) + 4
    • To find g(0), substitute x = 0 into the expression for g(x): g(0) = f(0) + 4
    • Calculate f(0) = (-6)(-2)(6) = 72
    • Therefore, g(0) = 72 + 4 = 76

    Function Definitions and Percentage Increases

    • For x > 0, the function f(x) is defined as 201% of x
    • This means that f(x) = 2.01 * x

    Solving for a Variable

    • Solve for k in the equation 14j - m = 5k
    • Divide both sides by 5: k = (14j - m) / 5

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    ASSIGNMENT Practice Test 3 S2M1 PDF

    Description

    Test your understanding of linear equations, including finding equations of lines, interpreting slopes and intercepts, and evaluating linear functions. This quiz covers concepts such as parallel lines, perimeters of squares, and practical applications of linear functions.

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