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Twelve Basic Functions
1.3 Twelve Basic Functions
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What you’ll learn about
What Graphs Can Tell You Twelve Basic Functions Analyzing Functions Graphically … and why As you continue to study mathematics, you will find that the twelve basic functions presented here will come up again and again. By knowing their basic properties, you will recognize them when you see them.
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The Identity Function Domain: Range: Asymptotes (if any):
Symmetry (if any): x-intercepts (Roots): y-intercepts (if any): Continuous (y/n): Periodic (y/n): Bounded (y/n):
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The Quadratic Function
Domain: Range: Asymptotes (if any): Symmetry (if any): x-intercepts (Roots): y-intercepts (if any): Continuous (y/n): Periodic (y/n): Bounded (y/n):
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The Cubic Function Domain: Range: Asymptotes (if any):
Symmetry (if any): x-intercepts (Roots): y-intercepts (if any): Continuous (y/n): Periodic (y/n): Bounded (y/n):
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The Reciprocal Function
Domain: Range: Asymptotes (if any): Symmetry (if any): x-intercepts (Roots): y-intercepts (if any): Continuous (y/n): Periodic (y/n): Bounded (y/n):
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The Square Root Function
Domain: Range: Asymptotes (if any): Symmetry (if any): x-intercepts (Roots): y-intercepts (if any): Continuous (y/n): Periodic (y/n): Bounded (y/n):
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The Absolute Value Function
Domain: Range: Asymptotes (if any): Symmetry (if any): x-intercepts (Roots): y-intercepts (if any): Continuous (y/n): Periodic (y/n): Bounded (y/n):
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The Exponential Function
Domain: Range: Asymptotes (if any): Symmetry (if any): x-intercepts (Roots): y-intercepts (if any): Continuous (y/n): Periodic (y/n): Bounded (y/n):
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The Natural Logarithm Function
Domain: Range: Asymptotes (if any): Symmetry (if any): x-intercepts (Roots): y-intercepts (if any): Continuous (y/n): Periodic (y/n): Bounded (y/n):
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The Greatest Integer Function
Domain: Range: Asymptotes (if any): Symmetry (if any): x-intercepts (Roots): y-intercepts (if any): Continuous (y/n): Periodic (y/n): Bounded (y/n):
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The Logistic Function Domain: Range: Asymptotes (if any):
Symmetry (if any): x-intercepts (Roots): y-intercepts (if any): Continuous (y/n): Periodic (y/n): Bounded (y/n):
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The Sine Function Domain: Range: Asymptotes (if any):
Symmetry (if any): x-intercepts (Roots): y-intercepts (if any): Continuous (y/n): Periodic (y/n): Bounded (y/n):
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The Cosine Function Domain: Range: Asymptotes (if any):
Symmetry (if any): x-intercepts (Roots): y-intercepts (if any): Continuous (y/n): Periodic (y/n): Bounded (y/n):
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Piecewise Function Example
Domain: Range: Asymptotes (if any): Symmetry (if any): x-intercepts (Roots): y-intercepts (if any): Continuous (y/n): Periodic (y/n): Bounded (y/n): 𝑦= 𝑥+4 , 𝑥 <−1 𝑥 2 , −1≤ 𝑥 ≤2 4, 𝑥 >2
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Homework Page 113 #1-24
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Functions
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Functions (cont’d)
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