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FunctionsAnd
Relations
Properties ofLinear
Functions
Equations of Linear
Functions
Linear FunctionsAs Models
Forms ofLinear
Functions
What is the definition of a relation?
Any set of ordered pairs.
What is the definition of a function?
For every input, there is exactly one output.
Is the following equation a function? If so, state the
range.
Y = x - 3
It is a Function
Range y > 0
In the function x + y = 2,over the domain -1 < x < 3, tell
the corresponding range.
R = {y: -1 < y < 3}
Tell the range and domain of the following relation
-9 7
8
-2
6
D = {x: -9 < x < 7}
R = {-2 < y < 8}
What is the effect on the graph of changing the x – coefficient?
It changes the tilt (slope) of the graph
What is the effect on the graph of changing the constant term?
It changes where the line crosses the y – axis.
Name an equation of a line that has a slope that is infinitely
large.
X = #
Name an equation of a line that does NOT have a y-intercept.
X = #
True or False
If a line has a positive slope, you must rise a certain
number of units and then run to the right a certain number of
units.
False
Find an equation in slope-intercept form of a line going
through the points (- 4, 5), (6, 10).
Y = .5x + 7
Write an equation of a line in standard form going through
the point (- 2, 7) and is perpendicular to 3x + 4y = 72.
- 4x + 3y = 29
Write an equation in slope-intercept form of a line that has an x-intercept of 5 and a slope
of – 2/3.
Y = -2/3x + 10/3
Write an equation in slope-intercept of a line containing
(5, 8) and is parallel to 2x + 3y = 9.
Y = -2/3x + 34/3
You have one hour to make cookies for your school bake sale. You spend 20 minutes
mixing the dough. It then takes 12 minutes to bake each tray of cookies. If you bake one tray at a time, what model can you
use to find how many trays you can bake?
12x + 20 = 60
Handy Andy sells 23 oz cans of ranch style beans for 63 cents and 15 oz cans for 45 cents. Assume that the price varies linearly with the number of
ounces.Write the particular equation in
slope intercept form.
C = 9/4w + 45/4
Handy Andy sells 23 oz cans of ranch style beans for 63 cents and 15 oz cans for 45 cents. Assume that the price varies linearly with
the number of ounces.
A 52 oz can costs $1.39. According to your model, is this can over or under – priced? By
how much?
Over – Priced by 11 cents.
Handy Andy sells 23 oz cans of ranch style beans for 63 cents and 15 oz cans for 45 cents. Assume
that the price varies linearly with the number of ounces.
Suppose that an “individual serving” can was priced at $0.21.
About how many oz. of beans would you expect to get?
4 oz
Handy Andy sells 23 oz cans of ranch style beans for 63 cents and 15 oz cans for 45
cents. Assume that the price varies linearly with the number
of ounces.
What is the weight intercept?
(- 5, 0)
Handy Andy sells 23 oz cans of ranch style beans for 63 cents and 15 oz cans for 45
cents. Assume that the price varies linearly with the number
of ounces.
What is the price intercept?
(0, 45/4)
Define slope-intecept form?
Y = mx + b, where m is the slope of the line and b is where
the line crosses the y-axis
True or False
There is only one slope-intercept form for each
equation.
True
A line only has one slope and crosses the y-axis in one spot.
True or False, if False, correct.
The definition of standard form is Ax + By = C, where A,B,C are
integers.
False,
A, B and C are constants
True or False
You can change slope-intercept form into point-slope
form.
True
Just get an ordered pair out of SIF and change to PSF.
True of False, correct if false.
The C is Standard Form ends up being your y-intercept of
your line.
False
C/B is y-intercept