CS代考 MTH130 Lesson 2.1 Increasing, Decreasing, and Piecewise Functions: Applicat

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MTH130 Lesson 2.1 Increasing, Decreasing, and Piecewise Functions: Applications
A. How do you find the domain?
1) Is it a fraction?
a. Set the denominator equal to zero and solve for x.

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b. Domain:  , ___ ___,
2) Is it an even index radical?
a. Set the inside expression  0 and solve for x.
b. Domain: ___, or it could be  , ___
3) All other expressions
a. Domain is all real numbers or: ,
Find the domain of the function in interval notation.
1. f(x)x7 2x 1
3. f(x) x4 x2 9
4. fx x x2 9

Lesson 2.1 Increasing, Decreasing, and Piecewise Functions: Applications
5. f(x) t4
6. f(x) 34x
7. f(x)t23t
8. hz z3 z2

Lesson 2.1 Increasing, Decreasing, and Piecewise Functions:
Applications
B. Increasing, Decreasing, Constant Intervals
Use the graph to find:
(a) The intercepts, if any
(b) The domain and range
(c) The intervals on which the function is increasing, decreasing or constant

Lesson 2.1 Increasing, Decreasing, and Piecewise Functions:
Applications
Piecewise Functions
Evaluate the function at the specified values:
3x f  x    0
 2 x 2  1
f  x    x 3
if x1 i f x   1
i f x   1
i f  2  x  1
Find f2 Find f1 Find f0
Find f1 Find f0 Find f1 Find f3
3x2 if1x4 

Lesson 2.1 Increasing, Decreasing, and Piecewise Functions: Applications
C. Sketch the graph of the piecewise defined function.
1x f  x    5
if x2 i f x  2
f  x    x
i f x  0 2x3 if x0
f  x    x 2 i f x  1 3 if x1

Lesson 2.1 Increasing, Decreasing, and Piecewise Functions: Applications
5 if x  0
f  x    x 2  1 i f 0  x  3
 x  3 i f x  3
fx3x if x0  4 i f x  0

Lesson 2.1 Increasing, Decreasing, and Piecewise Functions:
Applications
Maxima and Minima
Use the graph to find:
(a) The values, if any, at which f has a local maximum. What are these local maxima? (b) The values, if any at which f has a local minimum. What are these local minima?

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