# Chapter 2
### *2-1 Relations and Functions*:
\* a function rule is an equation that represents an output value in terms of an input value. You can write a function rule in the function notion
ex
\[Outputs: y, f(x), C, &, etc.
\[Inputs: x, or any other variables
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Flashcard 9
^^EX. Tickets to a concert are available online for $35 each plus a heading fee of $2.50. The total cost is a function of the number of tickets bought. What function rule models the cost of the concert tickets? Evaluate the function for 4 tickets.^^
Answer:
Independent = # of tickets bought (x)
Dependent = Total cost of everything (y)
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### *2-2 Direct Variation*:
You can write a formula for a direct variation function as y=kx, or y/x = k, where k = 0.
x represents input values, and y represents output values. The Formula y/x says that, except for (0,00, the radio of all output-input pairs equals the constant k, the constant of variation.
\
In direct variation, y/x is the same for __all__ pairs of data where x = 0. So \[y1/x1 = y2/x2\] is true for the ordered pairs (x1, y1) and (x2, y2), where neither x1 nor x2 is zero
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### *2-3 Linear function and Slope - Intercept Form:*
\[Slope - is also denoted with the letter __*m*__.
The slope is the “rate of change”.\]
a function whose graph is a line a linear function. You can represent a linear function with a linear equation, such as y=6x -4. A solution of a linear equation is any ordered pair (x,y) that makes an equation true.
There are different special forms of the linear equation: slope-intercept form and point-slope forms.
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### *2-4 0
y = f(x) + k
* translation down by k units, k>0
y = f(x) - k
* \
* **Vertical stretches and compressions**
* vertical stretch, a >1
y = af(x)
* vertical compressions, 0