Section 5.2B Power amd Piecewise Defined Functions Definition: A function is a function of the form kx r , where k and r are real numbers. Some Definitions Involving Exponents: 1. If a 6= 0, a 0 = 1, a -1 = 1 a , and, in general, a -x = 1 a x . 2. a 1/2 = p a, a 1/3 = 3 p a, and, in general, a 1/n = n p a. 3. a m/n = n p a m =( n p a) m The domain of f (x)= n p g(x) is all real numbers (-1, 1) if n is odd. If n is even then to find the domain of f (x)= n p g(x), you must solve g(x) ≥ 0 for x. Example 1: Find the domain of the following power functions: a) f (x)= 3 p x 2 - 1 a) f (x)= p x - 1 b) 4x - 2 4 p x - 1 power 3 is odd , so domain is (-o@ X - 120 Domain + I + I X Z / [@ Root function vs on the bottom of the fraction , so solve × - 1 > 0 for × ( Can't have * Obooytoathe ) ¥1 fiend
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Section 5.2B Power amd Piecewise Defined Functionsmayaj/m140_Chapter5_Sec5.2B_s18501.pdfSection 5.2B Power amd Piecewise Defined Functions Definition: A function is a function of
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Section 5.2B Power amd Piecewise Defined Functions
Definition: A function is a function of the form kxr, where k and r are
real numbers.
Some Definitions Involving Exponents:
1. If a 6= 0, a0 = 1, a�1 = 1a , and, in general, a�x = 1
ax .
2. a1/2 =pa, a1/3 = 3
pa, and, in general, a1/n = n
pa.
3. am/n = npam = ( n
pa)m
The domain of f(x) = npg(x) is all real numbers (�1,1) if n is odd. If n is even then to find
the domain of f(x) = np
g(x), you must solve g(x) � 0 for x.
Example 1: Find the domain of the following power functions:
a) f(x) = 3px2 � 1
a) f(x) =px� 1
b)4x� 24px� 1
power
3 is odd, so domain is (-o@
X - 120 Domain+ I + I
X Z / [@
Root function vs on the bottom
of the fraction , so solve × -1 > 0 for × ( Can't have * Obooytoathe)
¥1fiend
b)
px
x2 � 3x� 4
Example 2: Rationalize the numerator of the function
px+ 2� 5
x� 2
Example 3: Compute the following for the function defined below. Simplify your answers.
Definition: Functions whose definition involve more than one rule are calledPiecewise Functions.
To graph, graph each rule over the appropriate portion of the domain.
Example 4, Absolute value function: The absolute value of a number x, denoted by |x|,is the distance from x to 0 on the real number line. The plot and definition of absolute value
function if given below.
x
y
|x| =(x x � 0
�x x < 0
Example 5: Write f(x) = |6x+ 7| as a piecewise defined function.