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Algebra I Unit 5 Relationships

This document discusses linear relationships, continuous and discrete functions, and writing equations. It provides the following key points: 1) Linear relationships have one or two variables, no variables raised to powers greater than one, and graph as a straight line with a constant rate of change. 2) A function is continuous if its graph is an unbroken curve, and discrete if its values are separate. 3) Writing linear equations involves finding the slope using rise over run and finding the y-intercept from the table of values where x is zero. Exponential equations take the form y=(a)(b)^x, with a as the y-intercept and b as the ratio of terms.

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2K views8 pages

Algebra I Unit 5 Relationships

This document discusses linear relationships, continuous and discrete functions, and writing equations. It provides the following key points: 1) Linear relationships have one or two variables, no variables raised to powers greater than one, and graph as a straight line with a constant rate of change. 2) A function is continuous if its graph is an unbroken curve, and discrete if its values are separate. 3) Writing linear equations involves finding the slope using rise over run and finding the y-intercept from the table of values where x is zero. Exponential equations take the form y=(a)(b)^x, with a as the y-intercept and b as the ratio of terms.

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Linear Relationships

Have one or two variables.


No variable in the linear equation is raised
to a power greater than one or used as a
denominator in a fraction.
Linear equations have a constant rate of
change and graph as a straight line.
Slope intercept form Finding x-intercepts Finding y-intercepts Slope formula = change in y =
change in x
Parallel lines Perpendicular lines-

Continuous or Discrete

A function is continuos when it's graph is a


single unbroken curve.
A function is discrete when values are
separate or unconnected.

Writing Equations
Linear Equations

Linear equations will have a constant


change in x and in y.
Remember slope intercept form,
y = mx + b
Find m, m is the change in y over the change
in x.
m = change in y
change in x
Find the y-intercept, look at the table of
values and pick the y value where x is zero.
(0, b)

Exponential Equations

Exponential equations take the form


y = (a)(b )
Find a, look at the table of values and pick
the y value where x is zero. (0, a)
Find b, b is the ratio of the second term over
the first term.
b = second term
first term

Odd and Even Functions

End behavior- The behavior of the graph as X


approaches positive or negative infinity.
If the leading coefficient is positive, the
graph will end upward. If the leading
coefficient is negative, The graph will end
downward.
Even degree polynomial- A polynomial which
the highest exponent is an even number. Both
ends of the graph extend in the same
direction.
Odd degree polynomial- a polynomial
function which the highest exponent is an odd

number. One end of the graph will extend


upward and the other will extend downward.
Interval of increase- domain of increase
Interval of decrease- domain of decrease

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