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College Algebra Practice Test 3 Concepts

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  • How do you find the distance between two points P(x1, y1) and Q(x2, y2)?
    Use the distance formula: \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).
  • How do you find the midpoint of the segment connecting points P(x1, y1) and Q(x2, y2)?
    The midpoint is \(\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)\).
  • How do you graph a linear equation using intercepts?
    Find the x-intercept by setting y=0 and the y-intercept by setting x=0, then plot these points and draw the line through them.
  • How do you write the equation of a line given a point and slope?
    Use point-slope form: \(y - y_1 = m(x - x_1)\), then simplify as needed.
  • What is the domain of a relation?
    The set of all possible x-values (inputs) in the relation.
  • What is the range of a relation?
    The set of all possible y-values (outputs) in the relation.
  • How do you determine if a relation is a function?
    Check if each x-value corresponds to exactly one y-value; if yes, it is a function.
  • How do you evaluate a function f(x) at a specific value x = a?
    Substitute a into the function expression and simplify to find f(a).
  • How do you write the equation of a line in standard form?
    Standard form is \(Ax + By = C\), where A, B, and C are integers and A ≥ 0.
  • How do you find the equation of a line parallel to a given line through a point?
    Use the slope of the given line and the point to write the new line's equation using point-slope form.
  • How do you find intervals where a function is increasing, decreasing, or constant?
    Analyze the function's graph or derivative to identify intervals of increase, decrease, or constancy.
  • How do you evaluate a piecewise function at a given x-value?
    Determine which piece applies to the x-value and use that expression to find the function value.
  • What is the center-radius form of a circle's equation?
    It is \((x - h)^2 + (y - k)^2 = r^2\), where (h, k) is the center and r is the radius.
  • How do you find (f - g)(x) given functions f(x) and g(x)?
    Subtract the functions: (f - g)(x) = f(x) - g(x).
  • How do you find (f/g)(x) for functions f and g at a specific x?
    Calculate f(x) and g(x) separately, then divide: (f/g)(x) = f(x) / g(x), provided g(x) ≠ 0.
  • How do you find the composition (g ∘ f)(x)?
    Substitute f(x) into g: (g ∘ f)(x) = g(f(x)).
  • How do you sketch the graph of a parabola given by y = ax^2 + bx + c?
    Find the vertex, axis of symmetry, intercepts, and plot points to sketch the parabola.
  • How do you find the number of watches repaired to minimize cost given c(x) = 2x^2 - 176x + 86?

    Find the vertex of the parabola using \(h\left(x\right)=-\frac{b}{2a},k\left(y\right)=f\left(h\right)\)