September 16, 2011

1.3 Basic Functions

Identity Fn Squaring Fn Cubing Fn

Reciprocal Fn Square Root Fn Exponential Fn

Natural Logarithm Fn Sine Fn Cosine Fn

Absolute Value Fn Greatest Integer Fn Logistic Fn

f(x)=x f(x)=x2f(x)=x3

f(x)= 1x

f(x) = √x f(x) = ex

f(x) = ln xf(x) = sin x

f(x) = cos x

f(x) = x f(x) = int (x)

f(x) = 1

1 + e-x

September 16, 2011

Find the domain of each basic function.

September 16, 2011

Which of the functions have points of discontinuity?

September 16, 2011

Which functions are bounded (above and below)?

September 16, 2011

Which functions are even?

September 16, 2011

Graph the function: f(x) = sin (x) + 5

a. On what interval, if any, is the function increasing? decreasing?

b. Is the function odd, even, or neither?

c. Give the function's extrema, if any.

d. How does the graph relate to any of the 12 basic functions?

September 16, 2011

Piecewise Function: a function whose domain is divided into several parts and a different function rule is applied to each part.

f(x) = x2 if x ≤0 √x if x >0

September 16, 2011

Basic Function: ________________________

Domain: ____________________________________

Range: _____________________________________

Continuity: __________________________________

Increasing/Decreasing behavior: _________________

Symmetry: __________________________________

Boundedness: _______________________________

Local Extrema: _______________________________

Horizontal Asymptotes: ________________________

Vertical Asymptotes: __________________________

End behavior: ________________________________

f(x) = _____________

Identity

September 16, 2011

Basic Function: ________________________

Domain: ____________________________________

Range: _____________________________________

Continuity: __________________________________

Increasing/Decreasing behavior: _________________

Symmetry: __________________________________

Boundedness: _______________________________

Local Extrema: _______________________________

Horizontal Asymptotes: ________________________

Vertical Asymptotes: __________________________

End behavior: ________________________________

f(x) = _____________

Squaring

September 16, 2011

Basic Function: ________________________

Domain: ____________________________________

Range: _____________________________________

Continuity: __________________________________

Increasing/Decreasing behavior: _________________

Symmetry: __________________________________

Boundedness: _______________________________

Local Extrema: _______________________________

Horizontal Asymptotes: ________________________

Vertical Asymptotes: __________________________

End behavior: ________________________________

f(x) = _____________

Cubing

September 16, 2011

Basic Function: ________________________

Domain: ____________________________________

Range: _____________________________________

Continuity: __________________________________

Increasing/Decreasing behavior: _________________

Symmetry: __________________________________

Boundedness: _______________________________

Local Extrema: _______________________________

Horizontal Asymptotes: ________________________

Vertical Asymptotes: __________________________

End behavior: ________________________________

f(x) = _____________

Reciprocal

September 16, 2011

Basic Function: ________________________

Domain: ____________________________________

Range: _____________________________________

Continuity: __________________________________

Increasing/Decreasing behavior: _________________

Symmetry: __________________________________

Boundedness: _______________________________

Local Extrema: _______________________________

Horizontal Asymptotes: ________________________

Vertical Asymptotes: __________________________

End behavior: ________________________________

f(x) = _____________

Square Root

September 16, 2011

Basic Function: ________________________

Domain: ____________________________________

Range: _____________________________________

Continuity: __________________________________

Increasing/Decreasing behavior: _________________

Symmetry: __________________________________

Boundedness: _______________________________

Local Extrema: _______________________________

Horizontal Asymptotes: ________________________

Vertical Asymptotes: __________________________

End behavior: ________________________________

f(x) = _____________

Exponential

September 16, 2011

Basic Function: ________________________

Domain: ____________________________________

Range: _____________________________________

Continuity: __________________________________

Increasing/Decreasing behavior: _________________

Symmetry: __________________________________

Boundedness: _______________________________

Local Extrema: _______________________________

Horizontal Asymptotes: ________________________

Vertical Asymptotes: __________________________

End behavior: ________________________________

f(x) = _____________

Natural Logarithm

September 16, 2011

Basic Function: ________________________

Domain: ____________________________________

Range: _____________________________________

Continuity: __________________________________

Increasing/Decreasing behavior: _________________

Symmetry: __________________________________

Boundedness: _______________________________

Local Extrema: _______________________________

Horizontal Asymptotes: ________________________

Vertical Asymptotes: __________________________

End behavior: ________________________________

f(x) = _____________

Sine

September 16, 2011

Basic Function: ________________________

Domain: ____________________________________

Range: _____________________________________

Continuity: __________________________________

Increasing/Decreasing behavior: _________________

Symmetry: __________________________________

Boundedness: _______________________________

Local Extrema: _______________________________

Horizontal Asymptotes: ________________________

Vertical Asymptotes: __________________________

End behavior: ________________________________

f(x) = _____________

Cosine

September 16, 2011

Basic Function: ________________________

Domain: ____________________________________

Range: _____________________________________

Continuity: __________________________________

Increasing/Decreasing behavior: _________________

Symmetry: __________________________________

Boundedness: _______________________________

Local Extrema: _______________________________

Horizontal Asymptotes: ________________________

Vertical Asymptotes: __________________________

End behavior: ________________________________

f(x) = _____________

Absolute Value

September 16, 2011

Basic Function: ________________________

Domain: ____________________________________

Range: _____________________________________

Continuity: __________________________________

Increasing/Decreasing behavior: _________________

Symmetry: __________________________________

Boundedness: _______________________________

Local Extrema: _______________________________

Horizontal Asymptotes: ________________________

Vertical Asymptotes: __________________________

End behavior: ________________________________

f(x) = _____________

Greatest Integer

September 16, 2011

Basic Function: ________________________

Domain: ____________________________________

Range: _____________________________________

Continuity: __________________________________

Increasing/Decreasing behavior: _________________

Symmetry: __________________________________

Boundedness: _______________________________

Local Extrema: _______________________________

Horizontal Asymptotes: ________________________

Vertical Asymptotes: __________________________

End behavior: ________________________________

f(x) = _____________

Logistic

September 16, 2011