hjk Flashcards
What is a graph equation?
A graph equation is a mathematical expression that describes the relationship between variables in a graphical format.
True or False: A linear equation can be represented as a straight line on a graph.
True
Fill in the blank: The general form of a linear equation is ____.
y = mx + b
What does the ‘m’ represent in the equation y = mx + b?
‘m’ represents the slope of the line.
What is the purpose of the ‘b’ in the linear equation y = mx + b?
‘b’ represents the y-intercept of the line.
Multiple Choice: Which of the following is a quadratic equation? A) y = 2x + 3 B) y = x^2 - 4 C) y = 3x^3
B) y = x^2 - 4
What shape does a quadratic equation form when graphed?
A parabola.
True or False: The vertex of a parabola is the highest or lowest point on the graph.
True
Fill in the blank: The standard form of a quadratic equation is ____.
y = ax^2 + bx + c
What is the discriminant in the context of a quadratic equation?
The discriminant is the value of b^2 - 4ac, which determines the nature of the roots.
Multiple Choice: If the discriminant is positive, how many real roots does the quadratic equation have? A) Zero B) One C) Two
C) Two
What is the relationship between the roots of a quadratic equation and its graph?
The roots are the x-values where the graph intersects the x-axis.
True or False: A cubic equation can have up to three real roots.
True
Fill in the blank: The general form of a cubic equation is ____.
y = ax^3 + bx^2 + cx + d
What is a piecewise function?
A piecewise function is a function defined by multiple sub-functions, each applying to a certain interval of the main variable.
Multiple Choice: Which of the following represents a piecewise function? A) y = x^2 B) y = {x^2 for x < 0; x + 2 for x >= 0} C) y = 3x
B) y = {x^2 for x < 0; x + 2 for x >= 0}
What is the significance of the x-intercept in a graph?
The x-intercept is the point where the graph crosses the x-axis, indicating where the function equals zero.
True or False: The slope of a vertical line is undefined.
True
Fill in the blank: The slope of a horizontal line is ____.
0
What does it mean for a graph to be symmetric about the y-axis?
It means that for every point (x, y) on the graph, the point (-x, y) is also on the graph.
Multiple Choice: Which type of function is symmetric about the origin? A) Even function B) Odd function C) Neither
B) Odd function
What is the significance of transformations in graphing equations?
Transformations allow us to shift, stretch, compress, or reflect the graph of a function.
True or False: A vertical shift of a graph is achieved by adding or subtracting a constant from the output.
True
Fill in the blank: A horizontal shift of a graph is achieved by ____.
adding or subtracting a constant from the input.
What are asymptotes in the context of graphing rational functions?
Asymptotes are lines that the graph approaches but never touches or crosses.
Multiple Choice: Which type of asymptote can be vertical? A) Horizontal B) Vertical C) Both
C) Both
