Rates of Change
This term describes how much a quantity changes relative to another quantity.
What is rate of change?
This form of a quadratic shows its maximum or minimum clearly.
What is vertex form?
Clue: When a quadratic has no real roots, the solutions are found using this symbol.
What is i, the imaginary unit?
These occur where a rational function’s denominator equals zero.
What are vertical asymptotes?
Clue: Adding 3 to a function, as in f(x)+3f(x)+3, moves the graph in this direction.
What is up?
The average rate of change of a function over an interval is equivalent to this geometric concept.
What is the slope of the secant line?
The graph of any quadratic function is always this shape.
What is a parabola?
Complex solutions to real polynomials always come in these.
What are conjugate pairs?
A rational function’s end behavior is determined by the relationship between these.
What are the degrees of the numerator and denominator?
Reflecting a graph across the x-axis is equivalent to multiplying the function by this.
What is −1−1?
When the rate of change is constant, the function must be this type.
What is linear?
The linear term of a quadratic affects the location of this point on the graph.
What is the vertex?
The expression "the square root of negative nine" simplifies to this number.
What is 3i?
If both degrees are equal, the horizontal asymptote is this ratio.
What is the ratio of the leading coefficients?
In the transformation f(x−2)f(x−2), the graph moves this way.
What is right 2 units?
For a quadratic function, the rate of change itself changes at a constant rate, known as this.
What is the second difference?
A quadratic function whose leading coefficient is negative opens in this direction.
What is downward?
Clue: If a polynomial has degree 5, it must have this many total solutions counting complex ones.
What is 5?
A hole occurs when the numerator and denominator share this.
What is a common factor?
Multiplying the input by a number greater than 1, such as f(3x)f(3x), causes this type of change.
What is a horizontal compression?
Instantaneous rate of change approximates the slope of this type of line.
What is the tangent line?
This value, found using b2−4acb2−4ac, determines whether a quadratic has 0, 1, or 2 real solutions.
What is the discriminant?
A polynomial with complex zeros but real coefficients must have this relationship between its complex roots.
What is that they are conjugates?
If the numerator’s degree is exactly one more than the denominator’s degree, the function has this type of asymptote.
What is an oblique/slant asymptote?
This general term describes changes that move, stretch, flip, or shrink a graph.
What are transformations?