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MATH 1314 College Algebra

MATH 1314 College Algebra. Functions and their Graphs Section 3.1. Functions Section :_____. Relation from X into Y: a correspondence between set X and set Y. An X( domain ) can have one or more Y’s( range ).

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MATH 1314 College Algebra

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  1. MATH 1314 College Algebra Functions and their Graphs Section 3.1

  2. Functions Section :_____ • Relation from X into Y: a correspondence between set X and set Y. • An X(domain) can have one or more Y’s(range). • Function from X into Y: a relation from set X to set Y that associates each value of X to exactly one value of Y. • In a function, each X can only have one Y. • X is independent variable (input) • Y is dependent variable (output, Y depends on X)

  3. Functions Section :_____ • Relation or Function? Relation Function X Y 3 1 -6 -1 5 8 -1 5 8 -1 5 8 3 1 -6 X Y Function Relation X Y 3 1 -6 { (-4, 0) , (1, 9) , (0, -6) , (-8, 3) , (1, -2)}

  4. Functions Section :_____ • Function Notation • means “the value of function at the value of ”. • To evaluate at some -value means: • Substitute -value or expression into -variable of function and simplify result. • Example: If , find . • So when , then on graph of .

  5. Functions Section :_____ • Domainof : set of all x-values for which is defined. • x-values excluded from function domains are: • real numbers that cause division by zero • real numbers that cause negative expressions in even roots (Example: , , ...) • A way to find the domain of a function: • 1). Draw number line. • 2). Cross out excluded x-value(s) causing division by zero or even root of a negative number in f(x). • 3). Write domain from remaining x-axis in Interval Notation.If nothing is crossed out, then domain is .

  6. Functions Section :_____ • Find the domain of • is a rational function(Fraction). Can’t allow division by zero. • Find -values that cause division by zero. Set denominator and solve. , , • and cause division by zero in .Exclude them from domain. • 1). Draw number line. • 2). Exclude , • 3). Write domain of in Interval Notation.Answer: 0 0 0 5 5 5

  7. MATH 1314 College Algebra Functions and their GraphsSection 3.2

  8. Graphs of Functions Section :____ • A function can be identified from its graph bythe ____________________. • It states that if a vertical line can intersect a graph at more than one point, the graph is not a graph of a function. • Is this the graph of a function? Vertical-Line Test YES! NO!

  9. Graphs of Functions Section :____ • When information is needed about a function, such as how the variables relate to each other, its graph will usually let us see it more clearly. • If , then point is on graph of . If point is on graph of , then . • Example: Given function . Is point on graph of ? • When , . • So point is on graph of ; point is not.

  10. Graphs of Functions Section :___ • Information from the graph of a function. • Find . “find when is .” • Answer is .

  11. Graphs of Functions Section :___ • Use graph of function to find its domain. (Read all -values on graph from left to right.) • Answer: X=-21 X=18

  12. Graphs of Functions Section :___ • What is the range of ? (Read all y-values on graph from bottom to top.) • Answer: Y= 9 Y= -6

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