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What is a function?
A
function
f
is a set rule that assigns to each element
x
in aset
A
exactly one element, called
f(x)
in a set
B
What is the independant variable and what is the dependant variable of y =
f
(x)
y
is the dependant variable, &
x
independant variable
Squaring the fuction: f(x)=x
^{2 a) evaluate f(3), f(√5) b) find domain and range of f}
^{}
a) f(
3
)=
3
^{2 }
= 9, f (
√5
)=
√5
^{2}
=25
b) all real numbers f is ⎨y⎮y≥0, ⎬[0,∞)
Evaluating a Function: f(x) = 3x
^{2}
+ x - 5 ; f(-2)
f(
-2)
= 3(
-2
)
^{2}
+ (
-2
) - 5
= 12 - 2 -5
= 5
Evaluating a Function: f(x) = 2x
^{2}
+ 3x - 1
f(a)
f(-a)
f(a+h)
f(a+h) - f(a)
/h; h≠0
f(
a)
= 2
a
^{2}
+ 3
a
- 1
f(
-a
)=2
(-a)
^{2}
+3(
-a
)-1 =
2a
^{2}
-3a-1
f(
a+h
) = 2(
a+h)
^{2}
+3
(a+h)
- 1
= 2(a
^{2}
+2ah+h
^{2}
) +3a+3h - 1
= 2a
^{2}
+4ah+2h
^{2}
+3a+3h - 1
f
(a+h)
- f
(a)
/h
= (2a
^{2}
+4ah+2h
^{2}
+3a+3h - 1) -(2a
^{2}
+ 3a - 1)/h
= 2a
^{2}
+4ah+2h
^{2}
+3a+3h - 1 -2a
^{2}
- 3a + 1)/h
= 4ah+2h
^{2}
/h
= h(4a+2h)/h
= 4a+2h
Author
enrick
ID
92430
Card Set
enrick
Description
2.1 Functions
Updated
2011-06-30T10:40:20Z
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