2.4.2 Understanding properties of graphs

• What is the equation for a linear graph?

  y = mx + c
• What are the domain and range of a linear graph?

  All real numbers
• What are x-intercepts of a parabola?

  Points where graph crosses x-axis
• Which of the following equations represents a cubic function?

  $f(x) =$$x^3$
• In the cubic function $f(x) =$$ax^3 +$$bx^2 +$$cx +$$d$, what do the coefficients a, b, c, and d represent?


  Constants that determine the curve's shape
• What is another name for a quadratic graph?

  Parabola
• What is the equation of the axis of symmetry?

  x = 1
• Linear graphs continue endlessly in both directions.

  True
• What is the y-intercept of the graph?

  The y-intercept is -3.
• What is the value of the x-intercept?

  1
• A cubic graph always has two turning points.


  True
• The y-intercept is the point where the line crosses the y-axis.


  True
• Match the feature of a quadratic graph with its definition:

  Vertex ↔️ Lowest or highest point

  Axis of symmetry ↔️ Line dividing parabola in half

  X-intercepts ↔️ Points where graph crosses x-axis

  Y-intercept ↔️ Point where graph crosses y-axis
• What is the x-intercept of the graph?

  The x-intercept is 1.
• What is the general form of a cubic function?

  $f(x) =$$ax^3 +$$bx^2 +$$cx +$$d$
• What characteristics define the shape and behavior of a cubic function's graph?

  • A cubic function can have up to two turning points (local maxima or minima).
  • The graph extends to positive infinity in one direction and negative infinity in the other.
  • It may have up to three real roots (x-intercepts).
• What is the general form of a cubic function?

  $f(x) =$$ax^{3} +$$bx^{2} +$$cx +$$d$
• What is the maximum number of x-intercepts a cubic graph can have?

  3
• What are the coordinates of the vertex?

  (1, 2)
• What is the axis of symmetry of the graph?

  The axis of symmetry is the y-axis.
• Steps to transform the parent graph $y =$$\frac{1}{x^{2}}$ into $f(x) =$$\frac{1}{(x + 3)^{2}} +$$2$


  1️⃣ Shift left by 3 units

  2️⃣ Shift up by 2 units
• Cubic graphs exhibit vertical asymmetry.

  True
• What is the value of the y-intercept?

  -3
• Where does the y-intercept of a parabola occur?

  Graph crosses y-axis
• What defines a reciprocal graph?

  y equals 1 divided by a function of x
• The axis of symmetry divides a parabola in half.


  True
• Match the property with its definition:

  Slope ↔️ Steepness and direction of the line

  Y-intercept ↔️ Where the line crosses the y-axis

  Domain ↔️ All possible x-values

  Range ↔️ All possible y-values
• The graph of the parent reciprocal function looks the same as a linear graph.

  False
• How many graph types are compared in the study material?

  Four
• How many y-intercepts does a linear graph have?

  One
• What is the vertex of the graph?

  The vertex is at the point (1, 2).
• What are asymptotes in the context of reciprocal graphs?

  Lines the graph approaches
• Match the graph type with its shape:

  Linear ↔️ Straight line

  Quadratic ↔️ U-shaped (parabola)

  Cubic ↔️ S-shaped

  Reciprocal ↔️ Hyperbolic-like
• Which coefficient in a cubic function determines the curve's direction as x becomes large?


  a
• What type of symmetry does a quadratic graph have?

  Line symmetry through vertex