4-6 Functions and Linear Equations (pg 177-181)

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4-6 Functions and Linear Equations (pg 177-181)

• Standard PFA
• Indicator(s)
• P1 Represent patterns, rules and functions with
  words, tables, graphs, and variable expressions.
• P5 Recognize linear equations by plotting points
  in the coordinate plane
• P10 Analyze linear and non-linear relationships
  to show how changes in one variable results in
  the change of another

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Vocabulary

• Function- is an input/output relationship. You
  put a number in, perform the given function, and
  see what comes out.
• Function table- a table that organizes the input
  and output for a function
• Domain- the values that can go into a function
  (x)
• Range- the values that come out of a function (y)

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What is a linear equation?

• A linear equation has a graph that is a straight
  line.
• A linear equation looks like ymx b, where a
  and b are positive or negative numbers.
• m represents the slope of the line (we will
  discuss this more in the next section)
• b represents the y intercept (where the graphed
  line crosses the y axis)

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Graphing a linear equation
x 2x 1y y (x,y)
2 1y
2 1y
2 1y
2 1y

• Select a few values for x.
• Substitute and solve for y.
• Use each solution to write an ordered pair (x,y).

(2)
2 1 0 -1
5
(2,5)
(1)
3
(1,3)
1
(0)
(0,1)
-1
(-1)
(-1, -1)
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Graphing a linear equation (continued)

• Plot the points for the (x,y) pairs.
• Draw a line through the points you graphed.

x 2x 1y y (x,y)
2 2(2)1y 5 (2,5)
1 2(1)1y 3 (1,3)
0 2(0)1y 1 (0,1)
-1 2(-1)1y -1 (-1,-1)

• Notice the line crosses the y-axis at (0,1)

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• The four families of functions that you should
  know

Family Function (general) Example Shape of graph Table change
Linear ymx b y 3x y -2x 2
Quadratic yax2bxc y x2 y -2x2
Exponential y abx y 3x y (1/2)x
inverse y k x y 1 x
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• The four families of functions that you should
  know

Family Function (general) Example Shape of graph Table change
Linear ymx b y 3x y -2x 2 Line Add/ Subtract
Quadratic (non-linear) yax2bxc y x2 y -2x2 Parabola (U Shape) Change increases
Exponential (non-linear) y abx y 3x y (1/2)x Curve (half-pipe) Multiply/ divide
Inverse (non- linear) y k x y 1 x hyperbola Split graph xy k
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To which family do the following belong? y 4x
Exponential y 3x 7 Linear y
Inverse y 2x2 4 Quadratic