Rates of Change
The slope-intercept form of a linear equation is written in this format.
What is y=mx+by = mx + b?
The square root of −1-1 is represented by this symbol.
What is ii?
The slope-intercept form of a linear equation is written in this format.
What is y=mx+by = mx + b?
The line y=0y = 0 is often a horizontal asymptote when the numerator’s degree is this compared to the denominator’s.
What is smaller?
Subtracting 4 from a function, as in f(x)−4f(x) - 4, moves the graph in this direction.
What is down?
The axis of symmetry of a quadratic passes through this point.
What is the vertex?
The solutions to x2+1=0x^2 + 1 = 0 are these.
What are ii and −i-i?
The axis of symmetry of a quadratic passes through this point.
What is the vertex?
A rational function may cross its horizontal asymptote in this situation.
What is when the numerator and denominator degrees are equal?
Reflecting a graph across the y-axis is equivalent to replacing xx with this.
What is −x-x?
The product of the roots of a quadratic can be found using this formula.
What is ca\frac{c}{a}?
The complex number 3+4i3 + 4i has this magnitude. ?
What is 5?
The product of the roots of a quadratic can be found using this formula.
What is ca\frac{c}{a}?
The domain of a rational function excludes values that make this expression undefined.
What is the denominator?
In the transformation f(x+5)f(x + 5), the graph moves this way.
What is left 5 units?
A quadratic with no real solutions has its graph entirely in this position relative to the x-axis.
What is above or below the x-axis?
The Fundamental Theorem of Algebra guarantees that every polynomial of degree nn has this many roots.
What is nn (counting multiplicity)?
A quadratic with no real solutions has its graph entirely in this position relative to the x-axis.
What is above or below the x-axis?
If the numerator’s degree is greater than the denominators by two or more, the function has this type of end behavior.
What is unbounded growth or decline?
Multiplying the input by a fraction between 0 and 1, such as f(12x)f(\tfrac{1}{2}x), causes this type of change.
What is a horizontal stretch?
The sum of the roots of a quadratic equation can be found using this expression.
−ba-\frac{b}{a}?
The conjugate of the complex number a+bia + bi is written as this.
What is a−bia - bi?
The sum of the roots of a quadratic equation can be found using this expression.
What is −ba-\frac{b}{a}?
The process of dividing polynomials to determine asymptotes is called this.
What is polynomial long division?
The transformation that multiplies the entire function by a constant greater than 1 results in this.
What is a vertical stretch?