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Graphing Inequalities in Precalculus

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Terms in this set (20)

  • What is the first step in graphing an inequality?
    Replace the inequality symbol with an equal sign and graph the resulting equation.
  • When do you use a dotted line in graphing inequalities?
    Use a dotted line if the inequality is < or >, indicating the boundary is not included.
  • When do you use a solid line in graphing inequalities?
    Use a solid line if the inequality is ≤ or ≥, indicating the boundary is included.
  • How do you determine which side of the boundary line to shade?
    Choose a test point not on the boundary, plug it into the inequality, and shade the region where the inequality is true.
  • What is the solution to a system of inequalities?
    The intersection of the shaded regions that satisfy all inequalities in the system.
  • How is the inequality \(y \leq -2\) graphed?
    Graph the line y = -2 as a solid line and shade the region below it.
  • How do you graph a circle inequality like \((x - h)^2 + (y - k)^2 \leq r^2\)?
    Graph the circle with center (h, k) and radius r using a solid line and shade inside the circle.
  • What does a dashed parabola boundary indicate in an inequality?
    It indicates the inequality is strict (< or >), so the parabola itself is not included.
  • How do you graph the inequality \(y < x + 1\)?
    Graph the line y = x + 1 with a dashed line and shade below the line.
  • What does it mean if two inequalities have no intersection in their shaded regions?
    The system has no solution; the solution set is the empty set.
  • How do you graph vertical line inequalities like \(x \geq a\)?
    Graph the vertical line x = a as solid if ≥ or ≤, dashed if > or <, and shade the appropriate side.
  • What is the test point commonly used when shading inequalities?
    The point (0, 0) is often used unless it lies on the boundary line.
  • How do you graph the inequality \(x - y > -2\)?
    Graph the line x - y = -2 with a dashed line and shade the region where x - y > -2.
  • How do you graph the inequality \(x^2 + y^2 > 36\)?
    Graph the circle x^2 + y^2 = 36 with a dashed line and shade outside the circle.
  • How do you graph the inequality \(y \leq x^2 + 3\)?
    Graph the parabola y = x^2 + 3 with a solid line and shade below it.
  • What is the solution set for the system \(x + 2y \geq 2\) and \(x - y \leq 0\)?
    The intersection of the regions satisfying both inequalities, found by graphing each and shading their overlap.
  • How do you graph the system \(-x + 5y < 15\) and \(x \geq 2\)?
    Graph each inequality with appropriate boundary lines and shade the intersection of their solution regions.
  • What does shading below a line represent in an inequality?
    It represents all points where the y-values satisfy the inequality relative to the line.
  • What is the significance of the boundary line in graphing inequalities?
    It separates the coordinate plane into regions where the inequality is true or false.
  • Why is the test point (0,0) often chosen when graphing inequalities?
    Because it is easy to substitute and usually not on the boundary line.