Line 'EM Up
In the classic linear equation y = mx + b, the letter b represents this specific feature on a graph.
What is the y-intercept?
Compared to the basic parent function of a parabola, the graph of that same function minus five is shifted this many units in this direction.
What is down five units?
This is the only real number that cannot be used in the denominator of a rational function.
What is zero?
Spoken aloud as "f of g of x," this notation tells you to substitute one entire function into another.
What is function composition?
This term describes the highest or lowest point on a parabola, representing the maximum or minimum value of the quadratic function.
What is the vertex?
This is the slope of a line passing through the points (2, 5) and (4, 11).
What is 3?
To shift the graph of a function 3 units to the right, you would make this adjustment to the input variable x inside the function's argument.
What is replacing x with x - 3?
To find the x-intercept of a rational function, you set this part of the fraction equal to zero and solve.
What is the numerator?
If f(x) = x + 2 and g(x) = 3x, this is the simplified expression for f(g(x)).
What is 3x + 2?
This vertical, invisible line cuts a parabola perfectly in half, acting as a mirror line for every point on the graph.
What is the axis of symmetry?
This is the equation of a horizontal line passing through the point (-3, 7).
What is y = 7?
Multiplying the outside of a function by -1, as in g(x) = -f(x), results in a reflection across this axis.
What is the x-axis?
This is the vertical line value where an un-calculable gap occurs for a fraction with a numerator of x plus two and a denominator of x minus three.
What is x equals three?
The graphs of a function and its inverse are always symmetrical reflections across this diagonal line.
What is y = x?
If the leading coefficient of a quadratic function is a negative number, the resulting parabola will open in this direction.
What is downward?
Written as Ax + By = C, this two-word term describes this format of a linear equation.
What is standard form?
This transformation happens to the graph of f(x) when it is multiplied by a constant c where c > 1, as in g(x) = 2 f(x).
What is a vertical stretch?
Because you cannot take the square root of a negative value in the real number system, the expression inside the square root of x minus two must be greater than or equal to this number.
What zero?
This is the first algebraic step typically taken when finding the inverse of a function written as y = 2x + 5.
What is swapping x and y? (to get x = 2y + 5)
In a quadratic function, these specific points on the graph are found by setting the entire function equal to zero and solving for the input variable.
What are the x-intercepts? (also accept roots or zeros)
Two lines are perpendicular if their slopes have this relationship to each other.
What are negative reciprocals? (or opposite reciprocals)
Describe the two transformations that turn f(x) = |x| into g(x) = 2|x + 1|.
is a vertical stretch by a factor of 2 and a horizontal shift left 1 unit?
This is the horizontal line value that a fraction approaches at its far ends when the numerator is three x squared plus one and the denominator is x squared minus five.
What is y equals three?
For the function four x minus eight, its undoing inverse function can be described in words as x plus eight, all divided by this number.
What is four?
To find the horizontal coordinate of the turning point of a standard parabola, you can take the negative value of the middle term coefficient and divide it by twice this other coefficient.
What is the leading coefficient? (or the x-squared coefficient)?