Algebra Class: Functions and Graphs
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Questions and Answers

What is the set of all possible output values for a function known as?

  • Function
  • Set
  • Domain
  • Range (correct)
  • Which quadrant represents points where both x and y are negative?

  • Q III (correct)
  • Q II
  • Q IV
  • Q I
  • What condition is necessary for a relation to be classified as a function?

  • All values must be integers.
  • Every y-value must be paired with only one x-value.
  • Each x-value must be paired with two different y-values.
  • No x-value is paired with more than one y-value. (correct)
  • How can you determine if the domain includes a specific x-value for a function with a fraction?

    <p>Check if the denominator equals zero.</p> Signup and view all the answers

    What is the correct interval notation for a decreasing function from 4 to 5?

    <p>(4, 5)</p> Signup and view all the answers

    In the function f(x) = √(3x - 10), what is the domain of the function?

    <p>[10/3, ∞)</p> Signup and view all the answers

    Which statement correctly describes even functions?

    <p>Even functions have all powers of x as even numbers.</p> Signup and view all the answers

    In the piecewise function f(x) = 3x - 1 for x ≥ 0, what is the output when f(2) is calculated?

    <p>5</p> Signup and view all the answers

    Which interval indicates a constant function?

    <p>(0, 4)</p> Signup and view all the answers

    How is the graph of an odd function characterized?

    <p>It is symmetrical about the origin.</p> Signup and view all the answers

    What is the slope of the line given by the equation 3x + 4y = 12?

    <p>-3/4</p> Signup and view all the answers

    What is the y-intercept of the line represented by the equation 3x + 4y = 12?

    <p>3</p> Signup and view all the answers

    In the equation of a vertical line, how is the line represented?

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

    If a line has a slope of -4 and passes through the point (-1, 2), what is the equation of that line?

    <p>y = -4x - 2</p> Signup and view all the answers

    How do you find another point on a line using slope after plotting the y-intercept?

    <p>Move down 3 units and to the right 4 units.</p> Signup and view all the answers

    Which of the following is characteristic of odd functions?

    <p>All powers of x are odd</p> Signup and view all the answers

    Which expression represents an odd function?

    <p>$x^{3} + 2x$</p> Signup and view all the answers

    What type of functions are characterized by having a symmetry to the origin?

    <p>Odd functions</p> Signup and view all the answers

    Which of the following expressions is not an odd function?

    <p>$2x^{3} - 6x^{2} + 4x - 5x^{0}$</p> Signup and view all the answers

    What can be concluded about constant terms in odd functions?

    <p>They are absent in odd functions</p> Signup and view all the answers

    What characteristic do parallel lines share?

    <p>They have the same slope.</p> Signup and view all the answers

    What is the relationship between the slopes of perpendicular lines?

    <p>They are opposite and reciprocal.</p> Signup and view all the answers

    If two lines have slopes of 2 and -1/2, what can be said about them?

    <p>They are perpendicular.</p> Signup and view all the answers

    Which statement is true regarding parallel lines?

    <p>They always maintain the same slope.</p> Signup and view all the answers

    If a line has a slope of 3, which of the following slopes would form a line perpendicular to it?

    <p>-1/3</p> Signup and view all the answers

    What happens to the graph of f(x) when a negative sign is applied to the outside, resulting in -f(x)?

    <p>The graph flips downwards.</p> Signup and view all the answers

    When a function is transformed using f(x + #), what determines the new x-value of the graph?

    <p>The inside # is set to zero and solved.</p> Signup and view all the answers

    If a is greater than 1 in the transformation ay = f(x), how does this affect the graph?

    <p>The graph becomes taller and skinnier.</p> Signup and view all the answers

    When applying a transformation of f(-x), what is the resulting effect on the graph?

    <p>The graph reflects left to right.</p> Signup and view all the answers

    What is the effect on the graph when a number between 0 and 1 is used in front of the function, such as ay = f(x)?

    <p>The graph becomes shorter and fatter.</p> Signup and view all the answers

    What is the distance between the points (-2, 4) and (15, 6)? Round to the tenths.

    <p>7.3</p> Signup and view all the answers

    What is the midpoint of the points (4, 5) and (-2, -3)?

    <p>(1, 1)</p> Signup and view all the answers

    In the standard equation of a circle, what represents the center?

    <p>The point (h, k)</p> Signup and view all the answers

    What is the radius of the circle represented by the equation (x+3)² + (y-5)² = 36?

    <p>6</p> Signup and view all the answers

    What is the standard equation format of a circle with center at (0, -2) and radius of 1?

    <p>(x-0)² + (y+2)² = 1</p> Signup and view all the answers

    What is the domain of the function $f(x) = \frac{3x + 1}{x - 2}$?

    <p>$(-\infty, 2) \cup (2, \infty)$</p> Signup and view all the answers

    For the function $f(x) = \sqrt{3x - 12}$, which inequality must be satisfied to ensure the function is defined?

    <p>$3x - 12 \ge 0$</p> Signup and view all the answers

    What is the result of the composition $fog(x)$ where $f(x) = 3x - 5$ and $g(x) = 2x + 4$?

    <p>$6x + 7$</p> Signup and view all the answers

    What is the domain of the function $f(x) = x^2 - 2x - 15$?

    <p>$(-\infty, \infty)$</p> Signup and view all the answers

    Which of the following statements about the function $f(x) = \sqrt{3x - 12}$ is correct?

    <p>The function is defined for $x \ge 4$</p> Signup and view all the answers

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