Amy's Reflection #3

ok since almost everyone did inequalities...i thought i'd do something on domain & range...

Domain & Range of functions:

Polynomials:

the domain of all polynomials is (−∞, ∞).

For example:

f(x) = x^2 - 3x^2 + 2x - 1

D: (−∞,∞ )

f(x) = x^2 + 3

D:(−∞,∞ )

Fraction:

• you set the bottom to zero
• solve for x
• then set up intervals

For example:

f(x) = 1/x-2

x-2=0

x=2

D: (-∞ , 2) (2, ∞ )

Absolute Value:

D:(- ∞ , + ∞)

R: [0 , + ∞)

For example:

f(x) = |x + 8| - 9

D: (- ∞ , + ∞)
R: (-9, ∞)

f(x) = |x -7| + 5

D: (- ∞ , + ∞)
R: (5, ∞)

Square Roots:

to find the domain:

• set the inside = to zero
• then set a # line
  
• try values on either side of each #
• get ride of the negatives
• set up intervals

to find the range:

• graph

For example:

√9 - x^2

(solve for x...)

9 - x^2 = 0

-x ^2 = -9

√x^2 = √9

x = ±3

(# line)

(#s on either side..)

f(-4) = √9 - (-4)^2 = √-7
f(0) = √9 - (-4)^2 = √9
f(x) = √4 - (-4)^2 = √-7

√9 = ±3 so...

D: [-3, 3]

(graph....)

R: [0, 3]

*im pretty sure that's the range but...i might be reading the graph wrong
i hope i was able to help someone with this...