MAC1105library of functions piecewise-defined functions Sec PDF

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MAC1105library of functions piecewise-defined functions Sec...

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Library of Functions

MAC 1105

Library of Functions

Domain:

(−∞, ∞ ) Range: (−∞, ∞ )

Domain:

x-intercept (0,0) y-intercept (0,0) ODD Function

x-intercept (0,0) y-intercept (0,0) EVEN Function

Increasing:

Domain: Range:

( −∞, ∞)

(−∞, ∞ ) Range: [0, ∞)

( 0,∞) Decreasing: ( −∞,0)

Increasing:

( −∞, 0) ∪ ( 0, ∞) ( −∞, 0) ∪ ( 0, ∞)

None x-intercept None y-intercept ODD Function Decreasing: ( −∞, 0 ) ∪ (0, ∞ ) MDC Mathematics 1

Domain: (−∞, ∞ )

Domain: (−∞, ∞ )

Domain: [0, ∞)

Range: [0, ∞)

Range: ( −∞, ∞)

Range: [0, ∞ )

x-intercept (0,0) y-intercept (0,0) EVEN Function Increasing: ( 0,∞)

x-intercept (0,0) y-intercept (0,0) ODD Function Increasing: (−∞,∞ )

x-intercept (0,0) y-intercept (0,0) NEITHER Function Increasing: ( −∞,∞)

Decreasing: ( −∞,0)

Cube Root Function 3

f (x) = x Domain: (−∞, ∞ ) Range: ( −∞, ∞) x-intercept (0,0) y-intercept (0,0) ODD Function Increasing: ( −∞,∞)

MDC Mathematics 2

Piecewise-defined Functions A Piecewise-defined function is a function that is defined by two or more equations on different parts of its domain.

EXAMPLE 1a. Evaluate the function for the given values of x.

! x2 + 1 x < 0 f ( x) = " %x −1 x ≥ 0

f (−1) = _________

2a. Graph the function.

!1 " x +1 = f ( x) # 2 "&−x −1

! x2 + 3 x < 2 " h( x) = $7 2 ≤ x ≤4 " 2x − 1 x > 4 &

f ( 5) = ________

f (0 ) = _________

x 0 ! ! = !!!!!3!!!!!!!!!!!!"!! = 0!! !!!!!! ! !!!!!!!!!"!! < 0

! ! =

i) Find ! 2 ,!!!! 0 ,!!!!"#!! −1 ii) Locate any intercepts iii) Graph the function

−2! + 2!!!!"!! > 1 !!!!!!!1!!!!!!!!!!!"!! = 1!! !!!!!! ! !!!!!!!!!"!! < 1

i) Find ! 2 ,!!!! 0 , !(−1)!!!!"#!! 1 ii) Locate any intercepts iii) Graph the function

MDC Mathematics 4

EXAMPLE

YOUR TURN

4a. If

4b. If ! + 2!!!!!!!" − 2 ≤ ! < 1 ! ! = !!!!0!!!!!!!!!!!"!! = 1!!!!!!!!!!!!! !! !!−! + 2!!!!!!"!! > 1!!!!!!!!!!!!!!!! i) ii) iii) iv)

! + 3!!!!!!!" − 3 ≤ ! < 0 ! ! = !!!!1!!!!!!!!!!!"!! = 0!!!!!!!!!!!!! ! !!!−!!!!!!!!!!!!"!! > 0!!!!!!!!!!!!!!!!

Find the domain Locate any intercepts Graph the function Based on the graph, find the range

i) ii) iii) iv)

Find the domain Locate any intercepts Graph the function Based on the graph, find the range

MDC Mathematics 5...