1.1-1.4 Notes
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Transcript of 1.1-1.4 Notes
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8/7/2019 1.1-1.4 Notes
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1 .3 Linear Equations in two Variables
Slope of a line is a ratio of the difference in the vertical distanceto the horizontal distance between two points on that line.Slope can be represented many ways, such as: 2 1
2 1
y yrise ym
run x x x
There are four possible slopes of lines:Positive, which increases from left to rightNegative, which decreases from left to rightZero, which is horizontal (constant function)
Undefined or no slope, which is vertical
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Ex. Find the slope of the line which passes through thepoints (7, -1 ) and (-1 ,1 )
8 2
Ex. (-5, 6) and (1 0,4)
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Parallel lines have the same slopeSlopes of perpendicular lines are opposites and reciprocals
of each other
Ex. Find the slope of a line to the line which passes
through (2,-1 ) and (5,8).
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Three forms of equations of lines:Standard form Ax + By = CSlope-intercept form y = mx +bPoint-slope [you can use any point on the line for this]
To write the equation of a line, the minimum informationneeded is the slope and at least one point
1 1( )y y m x x
Ex. Write the equation of the line which passes through (4,-2)and is parallel to 3x - 4y = 1 0.
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Regression - fits data to an equation
1 . Enter the data into a blank tableSTAT Edit
2. Graph the scatterplot of the data
y = Turn PLOTon ZOOM 9 GRAPH
3. Fit to an equation: STAT CALC LinREG L1 , L2, Y1 ENTER
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1 .4 FunctionsA function of y in terms of x is a relation where every x value is paired
with exactly (one and only one) y value.
oNumerically as in a table or a list of points any repeated x values must bepaired with the same y values
oGraphically, a function must pass the vertical line test. As an imaginary
vertical line moves across the coordinate plane horizontally, the
graph of a function cannot intersect the vertical line more than
once.
oAlgebraically, an equation of a function must be able to be solved for ysuch that each x value inputted into the equation results in one
output.
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Ex. Is x + y = 1 6 a function?22
Function notation - solve for y, then replace y with f(x)
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Piecewise functions are literally pieces of functions put together to
make one new function. Here is an example of a piecewise
function to show how to write the algebraic representation of it:
and here is the graphical representation of it:
2
9, 3
( ) , 3 2
13, 2
2
x
f x x x
x x
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Domain of a function is the set of all x values (input) that havecorresponding real y values
Domain restrictions:
Square roots ( or any root with even index) Rational expressions Logarithmic functions (Ch. 3) Some trig functions (Ch. 4-6)
Ex. Find the domain of:
1 . f(x) =
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