1.4 - 1.6
In the slope-intercept form y = mx + b, this variable represents the "rise over run" or the rate of change of the line.
What is the slope? (m)
If f(x) = 2x2 + 5x and g(x) = x2 - 7x + 9, what is the resulting expression for (f - g)(x)?
What is x2 + 12x - 9?
This test is used to determine if a function is one-to-one; if any line drawn this way intersects the graph more than once, the function does not have an inverse.
What is the Horizontal Line Test?
If f(x) = -2x4 + 3x2 + 1, what is the end behavior of the graph according to the Leading Coefficient Test?
Both sides point to negative infinity, because it's negative even.
According to the Fundamental Theorem of Algebra, how many complex zeros (including repetitions) does the polynomial function f(x) = x4 - 3x2 + 5 have?
What is 4? (The degree of the polynomial determines the number of zeros).
These are the x-values for which f(x) = 0; they are also the x-coordinates of the points where a graph crosses the x-axis.
What are the zeros/x-intercepts of a function?
To obtain the graph of h(x) = (x + 2)3 + 1 from the parent function f(x) = x3, you must perform these two specific shifts.
What are a horizontal shift left 2 units and a vertical shift up 1 unit?
For the quadratic function f(x) = -x2 + 6x + 3, what is the vertex (h, k)?
What is (3, 12)?
When setting up the long division problem (x3 - 1) divided by (x - 1), how must you rewrite the dividend to ensure all terms are aligned correctly?
What is x3 + 0x2 + 0x - 1?
Using the Rational Zero Test for f(x) = x3 - 7x - 6, what is the complete list of all possible rational zeros?
What is + or - 1, 2, 3, and 6?
This specific parent function has a "V-shaped" curve, a domain of all real numbers, and is decreasing on the interval (-∞, 0) and increasing on (0, ∞).
What is the Absolute Value function? (f(x) = |x|)
Given f(x) = 2x2+ 5x and g(x) = x - 7, find (f ○ g)(x)
Hint: It involves substituting the entire function g(x).
What is 2x2 - 23x + 63?
If f(x) = (x - 4) /7, what is its inverse function, f-1(x)?
What is f-1(x) = 7x + 4?
For the function f(x) = (x + 1)2(x - 2), identify the two x-intercepts and state whether the graph crosses or touches the x-axis at each point based on their multiplicity.
What is the intercepts are (-1, 0) and (2, 0). At x = -1, the graph touches the axis (multiplicity 2); at x = 2, the graph crosses the axis (multiplicity 1)?
What are the equations for the vertical and horizontal asymptotes of the rational function f(x) = (3x - 6) / x + 5?
x = -5 (Vertical) and y = 3 (Horizontal).
A function is classified as this if f(-x) = f(x), resulting in a graph that is symmetric with respect to the y-axis.
What is an even function?
If $f(x) = x2 - 7x + 3 and g(x) = 4x - 1, what is the numerical value of the product (g · f)(x) when x = 0?
What is -3?
If the domain of a function f(x) is [-2, 5] and its range is [0, 10], what are the domain and range of its inverse function f-1(x)?
What is a domain of [0, 10] and a range of [-2, 5]
When using synthetic division to divide (x4 - 10x2 - 2x + 4) by (x + 3), what is the resulting quotient?
What is x3 - 3x2 - x + 1 (with a remainder of 1)?
For any rational function f(x), what is the specific procedure used to find and plot the y-intercept?
What is evaluating the function at f(0) (or setting x = 0 and solving for y)?
This mathematical rule states that for every single input (x), there can be only one specific output (y). You can quickly check this on a graph by ensuring that no vertical line crosses the curve more than once.
What is a function?
For the functions f(x) = -8x - 2 and g(x) = 5 - 4x, identify the domain of the quotient function (f / g)(x) in interval notation.
What is (-∞, 5/4) ∪ (5/4, ∞)?
For the quadratic function f(x) = 4x2 - 5x + 1, what is the x-coordinate (h) of the vertex?
What is 5/8?
What is the polynomial function f(x) in general form that has the real zeros 0, -2, and -4?
What is f(x) = x3 + 6x2 + 8x?