Chpt. 2, Functions, Equations, Graphs Flashcards
relation
A set of ordered pairs.
domain
The set of all inputs, or x-coordinates, in a relation of ordered pairs.
range
The set of all outputs, or y-coordinates, in a relation of ordered pairs.
function
A relation in which each element of the domain corresponds to exactly one element of the range.
vertical line test
This can be used to determine if one is dealing with a function or not. In this test, a line should be able to be drawn vertically at any point in the graph that hits only 1 point on the graph.
function rule
This represents an output value in terms of an input value.
function notation
This is when you name the function F, and when you write it out, you use the variables “F(x)” in place of the y-value. It does not mean “f times x.
independent variable
The input value, generally represented by “x.”
dependent variable
The output value, generally represented by “y.”
direct variation
A linear function defined by an equation of the form y = kx, where k does not equal 0.
constant of variation
The ratio of the two variables in a direct variation and the product of the two variables in an inverse variation.
slope
The slope of a non-vertical line is the ratio of the vertical change to the horizontal change between points. Slope can be calculated by finding the difference in the y-coordinates to the ratio of the x-coordinates for any two points on the line. The slope of a vertical line is undefined.
linear function
A function whose graph is a straight line; these can be represented with linear equations.
linear equation
An equation of two variables that can be written in the form Ax + By = C, in which A, B, and C are all whole number, and in which both x and y cannot be 0 concurrently, but either can individually. Additionally, both A, B, and C must all represent real numbers. If the equation fits this form, it is linear. This form is referred to as standard form.
x-intercept, y-intercept
The point at which a line crosses the x- or y- axis.
slope-intercept form
The form of writing an equation that is as follows: y = mx +b, where y is the output variable, m is the slope, x is the input variable, and b is the constant of variation as well as the y-intercept..
zero slope; undefined slope
Described by a vertical line at x = #; described by a horizontal line at y = #.
point-slope form
The point-slope form for a non-vertical line with slope m is: (y1 - y2) = m(x1 - x2). Once one variable is known, plug it into this equation, and then transform the equation into slope-intercept form. Once this is done, you will have your b-value as well.
parallel lines
Coplanar lines that do not intersect. In the coordinate plane, parallel lines have the same slope.
perpendicular lines
Lines that intersect to form right angles. In the coordinate plane, these types of lines have slopes with a product of -1 (the slopes are reciprocals of each other with the opposite sign… call them opposite reciprocals, inverse reciprocals?).
scatter plot
A graph that relates two different sets of data by plotting the data as ordered pairs.
correlation
Indicates the strength of a relationship between two data sets.
line of best fit
The trend line that gives the most accurate model of related data.
correlation coefficient
The correlation coefficient, “r,” indicates the strength of the correlation. The more close the value of r is to 1 or -1, the more closely the data resembles a line, and the more accurate the model is likely to be.
parent function
The simplest form of a set of functions that form a family. For example, y = x is the parent function for functions of the form, y = x + k.
transformation
A transformation of a function y = af(x-h) + k is a change made to at least one of the value, a, h, and k. the four types of transformations are dilation, reflections, rotations, and translations.
translation
Shifts that graph of a parent function horizontally, vertically, or both without changing it’s shape or orientation.
reflection
Flips the graph of a function across a line, such as the x or y axis. Each point on the graph of the reflected function is the same distance from the line of reflection as is the corresponding point on the graph of the original function.
vertical stretch
A vertical stretch multiplies all y-values of a function by the same factor greater than 1.
vertical compression
Reduces all y-values of a function by the same factor between 0 and 1.
how to: vertical translations
y = f(x) + k;
translation when k > 0
translation when k < 0
how to: horizontal translation
y = f(x -h);
right when h > 0
left when h < 0
how to: vertical stretches and compressions
y = af(x)
stretch when a > 1
compression when 0 < a < 1
how to: reflections
in the x-axis:
y = -f(x)
in the y-axis
y = f(-x)
absolute value function
A function of the form f(x) = absval(mx + b) + c, where m does not equal 0.
axis of symmetry
The line that divides a figure into two parts that are mirror images.
vertex
A point where a function reaches it’s maximum or minimum value.
linear inequality
A graph in two variables whose graph is a region of the coordinate plane that is bounded by a line.
boundary
A line in the coordinate plane on the graph of an inequality that separates solutions from non-solutions. The line itself may or may not consist of solutions. If it does, then the line is graphed as a solid line; if not, as a dotted line.
half-plane
The set of points in the coordinate plane that are on one side of the graph of a linear inequality.
test point
A point that is picked on one side of the boundary of the graph of a linear inequality. If the test point makes the inequality true, then all points on that side of the boundary are solutions of the inequality. If it makes it false, then all points on the other side of the boundary are solutions to the inequality.
