Chpt. 2, Functions, Equations, Graphs

Question 1

relation

Answer 1

A set of ordered pairs.

Question 2

domain

Answer 2

The set of all inputs, or x-coordinates, in a relation of ordered pairs.

Question 3

range

Answer 3

The set of all outputs, or y-coordinates, in a relation of ordered pairs.

Question 4

function

Answer 4

A relation in which each element of the domain corresponds to exactly one element of the range.

Question 5

vertical line test

Answer 5

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.

Question 6

function rule

Answer 6

This represents an output value in terms of an input value.

Question 7

function notation

Answer 7

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.

Question 8

independent variable

Answer 8

The input value, generally represented by “x.”

Question 9

dependent variable

Answer 9

The output value, generally represented by “y.”

Question 10

direct variation

Answer 10

A linear function defined by an equation of the form y = kx, where k does not equal 0.

Question 11

constant of variation

Answer 11

The ratio of the two variables in a direct variation and the product of the two variables in an inverse variation.

Question 12

slope

Answer 12

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.

Question 13

linear function

Answer 13

A function whose graph is a straight line; these can be represented with linear equations.

Question 14

linear equation

Answer 14

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.

Question 15

x-intercept, y-intercept

Answer 15

The point at which a line crosses the x- or y- axis.

Question 16

slope-intercept form

Answer 16

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..

Question 17

zero slope; undefined slope

Answer 17

Described by a vertical line at x = #; described by a horizontal line at y = #.

Question 18

point-slope form

Answer 18

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.

Question 19

parallel lines

Answer 19

Coplanar lines that do not intersect. In the coordinate plane, parallel lines have the same slope.

Question 20

perpendicular lines

Answer 20

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?).

Question 21

scatter plot

Answer 21

A graph that relates two different sets of data by plotting the data as ordered pairs.

Question 22

correlation

Answer 22

Indicates the strength of a relationship between two data sets.

Question 23

line of best fit

Answer 23

The trend line that gives the most accurate model of related data.

Question 24

correlation coefficient

Answer 24

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.

Question 25

parent function

Answer 25

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.

Question 26

transformation

Answer 26

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.

Question 27

translation

Answer 27

Shifts that graph of a parent function horizontally, vertically, or both without changing it’s shape or orientation.

Question 28

reflection

Answer 28

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.

Question 29

vertical stretch

Answer 29

A vertical stretch multiplies all y-values of a function by the same factor greater than 1.

Question 30

vertical compression

Answer 30

Reduces all y-values of a function by the same factor between 0 and 1.

Question 31

how to: vertical translations

Answer 31

y = f(x) + k;

translation when k > 0
translation when k < 0

Question 32

how to: horizontal translation

Answer 32

y = f(x -h);

right when h > 0
left when h < 0

Question 33

how to: vertical stretches and compressions

Answer 33

y = af(x)

stretch when a > 1
compression when 0 < a < 1

Question 34

how to: reflections

Answer 34

in the x-axis:

y = -f(x)

in the y-axis

y = f(-x)

Question 35

absolute value function

Answer 35

A function of the form f(x) = absval(mx + b) + c, where m does not equal 0.

Question 36

axis of symmetry

Answer 36

The line that divides a figure into two parts that are mirror images.

Question 37

vertex

Answer 37

A point where a function reaches it’s maximum or minimum value.

Question 38

linear inequality

Answer 38

A graph in two variables whose graph is a region of the coordinate plane that is bounded by a line.

Question 39

boundary

Answer 39

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.

Question 40

half-plane

Answer 40

The set of points in the coordinate plane that are on one side of the graph of a linear inequality.

Question 41

test point

Answer 41

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.