Functions

Function

A function is when every X input has a Y input. For ex: (1,1) (2,2)

quadratic function

A function that can be written in the form f(x) = ax2+bx+c, where a,b,and c are real numbers and a ≠ 0 For ex: y=x^2

scatter plot

A graph with points plotted to show a possible relationship between two sets of data. For ex: Image

correlation

A measure of the relationship between two variables. For ex: Image

Indirect variation

If y = a/x, where a is constant, the relationship between x and y is called an indirect variation and the graph is a hyperbola. For ex: y=k/x

Independent variable

The experimental factor that is manipulated; the variable whose effect is being studied. For ex: X axis on coordinate plane

Continuous

going on without stopping on graph. For ex: constantly increasing

direct function

linear function described by y = mx or f(x) = mx For ex: y=kx

point-slope form

y-y1=m(x-x1) For ex: y=mx+b

slope-intercept form

y=mx+b, where m is the slope and b is the y-intercept of the line. For ex: y=mx+b

inverse function

A function in which two variables are inversely proportional. For ex: y=k/x

quadratic regression

A statistical method used to fit a quadratic model to a given data set. For ex: image

standard form

Ax + By=C, where A, B, and C are not decimals or fractions, where A and B are not both zero, and where A is not a negative For ex: Ax+By=C

one-to-one

Each entity in the relationship will have exactly one related entity. For ex: Image

Relations

Is a set of ordered pairs For example: (x,y) (1,15)

Vertical line test

Is a test used to determine whether a relation is a function by checking if a vertical line touches 2 or more points on the graph of a relation. For ex: *image*

Relative maximum

The highest point in a particular section of a graph. For ex: the highest point on graph.

Relative minimum

The lowest point in a particular section of a graph. For ex: lowest point on graph

Extrema

The maximum and minimum values of a function For ex: the y-value of the vertex.

exponential function

a function of the form f(x) = ab^x, where a and b are real numbers with a ≠ 0, b>0, and b ≠ 1. For ex: a ≠ 0, b>0, and b ≠ 1.

absolute value function

a function written in the form y = /x/, and the graph is always in the shape of a v For ex: f(x)=|x|

trend line

a line on a scatter plot drawn near the points. it shows a correlation For ex: Image

exponential regression

a method used to find an exponential function that models a set of data. For ex: y=a*b^x a=In(y)

arithmetic sequence

a sequence in which each term is found by adding the same number to the previous term For ex: Image

line of best fit

a smooth line that reflects the general pattern in a graph For ex: Image

linear regression

a statistical method used to fit a linear model to a given data set For ex: y=a+bx

dependent variable

a variable (often denoted by y ) whose value depends on that of another. For ex: Y axis

recursive formula

each term is formulated from one or more previous terms. For ex: image.

explicit formula

expresses the nth term of a sequence in terms of n For ex: image

parent function

the most basic function of a family of functions For ex: or the original function before a transformation is applied

Constant of variation

the number k in equations of the form y=kx For ex: y=kx

X-intercept

the x-coordinate of a point where a graph crosses the x-axis For ex: where the graph crosses the x-axis.

y-intercept

the y-coordinate of a point where a graph crosses the y-axis. For ex: *Image*

Discrete

unconnected graph. For ex: disconnected graph