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College Algebra Midterm Review

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  • Write a quadratic equation with solution set {2, -1} in general form.
    The quadratic equation is \(x^2 - 3x - 2\).
  • Solve the inequality (9x + 2)/(-5) ≤ 3x + 2 and express the solution in interval notation.
    The solution set is (-∞, -1/2].
  • Determine if the relation {(1, 11), (1, 22), (3, 8), (3, 10)} is a function and find its domain and range.
    It is not a function because x = 1 and x = 3 have multiple y-values.
  • Given the table of x and y values: x = {-5, -9, -17}, y = {5, 9, 17}, is this a function? Find domain and range.
    It is a function with domain {-5, -9, -17} and range {5, 9, 17}.
  • Write the equation of a line with slope -2 passing through (-3, -1/3) in slope-intercept form.
    The equation is \(y = -2x - \frac{19}{3}\).
  • Find the equation of a circle with center (-8, -16) and radius √8 in standard form.
    The equation is \((x + 8)^2 + (y + 16)^2 = 8\).
  • Describe the transformation of h(x) = 3√(x + 4) from f(x) = √x.
    h(x) is a horizontal shift 4 units left and vertical stretch by 3 of f(x).
  • Graph the absolute value function g(x) = -|5x + 5| + 3/2 as a transformation of f(x) = |5x|.
    g(x) is a reflection over the x-axis, vertical shift up by 3/2, and horizontal shift left by 1.
  • Find (f - g)(-2) given graphs of f and g.
    The value of (f - g)(-2) is 11.
  • Given f(x) = 7x - 2 and g(x) = x + 10, find (fg)(x) and its domain.
    (fg)(x) = \(7x^2 + 2\) with domain (-∞, ∞).
  • Write the vertex form of a parabola with vertex (-1, -1) and same shape as f(x) = 1/3 x^2.
    The equation is \(y = \frac{1}{3}(x + 1)^2 - 1\).
  • Identify zeros of f(x) = x^3 + 13x^2 - 14 given 1 is a zero.
    Other zeros are \(-7 + \sqrt{35}\) and \(-7 - \sqrt{35}\).
  • Describe the end behavior of f(x) = 2x^4 - 19x^3 - 2x^2 + 3x - 2 using the Leading Coefficient Test.
    The graph falls to the left and rises to the right.
  • Find the rational function with x-intercept (0,0), vertical asymptotes x = -2 and x = 2, and horizontal asymptote y = 0.
    The function is \(f(x) = \frac{x}{(x - 2)(x + 2)}\).
  • As x approaches 6 from the left, what is the behavior of f(x) in the given rational function graph?
    As x → 6-, f(x) → -∞.
  • What is the domain of the rational function f(x) = (7x^2 - 6x - 16)/(4x^2 - 5x)?
    Domain is all real numbers except x = 0 and x = 5/4.
  • What are the vertical and horizontal asymptotes of f(x) = (7x^2 - 6x - 16)/(4x^2 - 5x)?
    Vertical asymptotes at x = 0 and x = 5/4; horizontal asymptote at y = 7/4.
  • How do you determine if a relation is a function from a set of ordered pairs?

    If each x-value corresponds to exactly one y-value, it is a function.

    \(9\phi\)

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