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Chapter 1 - 2.2 Summary and vocabulary review
Here is a list of topics that you should already know.
Set of numbers:
Natural numbers – N Integers – Z Rational numbers – Q - fractions
Irrational numbers – I – Includes nonrepeating nonterminating decimals, ∏.
Real numbers – R – All of the above sets.
Scientific notation: A real number is written as _._ _ X 10n
Percent change: If a quantity changes from A to B then % change equals
X 100
Problem solving: Two common problem solving strategies are making a sketch or using a formula.
Mean and Median: Mean is the average of a set of numbers, i.e. if you want to find the average of
your five test grades you would add the five test grades together and divide by the number of test
there are, in this case five. Median is the middle number of a sequence that is in numerical order.
However, if there are two numbers that are exactly in the center then the median is the average of
those two numbers.
Relation, domain, and range: A relation is set of ordered pairs. Domain is a set of all the x-values in
the given relation. Range is the y-values in a given relation.
Cartesian (rectangular) coordinate system or xy-plane: This plane has four quadrants and is used to
plot ordered pairs.
Distance formula: The distance between two points (x1, y1) and (x2, y2) is
d=
Midpoint formula: The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is
M=
Scatter plot and line graph: A scatterplot consists of a set of ordered pairs plotted in the xy-plane.
When consecutive points are connected with line segments; a line graph results.
Function: A function computes exactly one output for each input.
Representations of a function: There are four representations of a function – verbal, symbolic, tabular,
and graphical. (See 4 representations handout)
Slope: The slope m of the line passing through points (x1,y1) and (x2,y2) is the change in y over the
change in x. (Sometimes also called “rise over run”)
m=
Ex) Find the slope between the points (-3, 5) and (2, -4)
Constant function: Given by f(x) = b, where b is a constant and its graph is a horizontal line. Given x =
b, where b is a constant and its graph is a vertical line.
Linear function: Given f(x) = mx + b and its graph is a nonvertical line; where m is the slope of the line
and b is the y-intercept of the line (place where it hits the y-axis) – (see WS: mx+b handout)
Nonlinear function: This function is not a line and cannot be represented as f(x) = mx + b
Linear model: If a quantity increases or decreases by a constant amount for each unit increase in x,
then it can be modeled by a linear function given by
f(x) = (constant rate of change)x + (initial amount)
Linear regression: Sometimes data does not fit in a nice linear equation; we can use regression to
model the data with a line of best fit.
Point-slope form: If a line passes through (x1, y1) and you know that slope is m then
f(x) = m(x-x1) + y1
***Use this when you know a point and the slope, or if you know two points on the line!!***
Slope-intercept form: If a line has slope m and y-intercept b, then
f(x) = mx + b
***Use this when you are given the y-intercept and a point on the line, or if you are given the y-intercept and the slope***
Determining intercepts:
To find the x - intercept(s), let f(x) = y = 0 in the equation and solve for x.
To find the y - intercept(s), let x = 0 in the equation and solve for f(x) = y.