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LIBRARY OF FUNCTIONS DAY 4 1. Linear Function
Domain: ________
x-intercept: ________ y-intercept: ________
even / odd / neither
incr’g on ________ decr’g on ________
local min @________ local max @________
2. Constant Function
Domain: ________
x-intercept: ________ y-intercept: ________
even / odd / neither
incr’g on ________ decr’g on ________
local min @________ local max @________
3. Identity Function
Domain: ________
x-intercept: ________ y-intercept: ________
even / odd / neither
incr’g on ________ decr’g on ________
local min @________ local max @________
4. Quadratic (Square) Function
Domain: ________
x-intercept: ________ y-intercept: ________
even / odd / neither
incr’g on ________ decr’g on ________
local min @________ local max @________
5. Cube Function
Domain: ________
x-intercept: ________ y-intercept: ________
even / odd / neither
incr’g on ________ decr’g on ________
local min @________ local max @________
6. Square Root Function
Domain: ________
x-intercept: ________ y-intercept: ________
even / odd / neither
incr’g on ________ decr’g on ________
local min @________ local max @________
7. Cube Root Function
Domain: ________
x-intercept: ________ y-intercept: ________
even / odd / neither
incr’g on ________ decr’g on ________
local min @________ local max @________
8. Reciprocal Function
Domain: ________
x-intercept: ________ y-intercept: ________
even / odd / neither
incr’g on ________ decr’g on ________
local min @________ local max @________
9. Absolute Value Function
Domain: ________
x-intercept: ________ y-intercept: ________
even / odd / neither
incr’g on ________ decr’g on ________
local min @________ local max @________
10. Greatest Integer Function
Domain: ________
x-intercept: ________ y-intercept: ________
even / odd / neither
incr’g on ________ decr’g on ________
local min @________ local max @________
h(x) = − 32
x + 1; x < 4
− 2; x ≥ 4
⎧⎨⎪
⎩⎪
g(x) =2x + 5; x ≥ − 313
x + 4; x < − 3
⎧⎨⎪
⎩⎪
Piecewise Functions DAY 4 Piecewise-defined Functions – A function that is defined in different ways for different parts of its domain. Step 1. Graph the boundary line. Step 2. Graph equation 1 (only over the correct domain). Step 3. Graph equation 2 (only over the correct domain). Step 4. Check that: The graph is a function! There is an open circle where it should be! 1. This is an example of a piecewise function: YOU TRY Graph the piecewise functions
2. 3.
1
2
f (x) =
x + 2; x < 1− x; x ≥ 1
⎧⎨⎩
Ex. 1) Evaluate the function at the given values:
f x( ) = 4x −3, if x > 35x + 2, if x ≤ 3⎧⎨⎪
⎩⎪
a. f −2( ) b.
f 3( ) c.
f 5( )
Ex. 5): Graph
f (x )=2x −1, − 2< x < 2
1, x = 2x 2 −3, x > 2
⎧
⎨⎪⎪
⎩⎪⎪
a. Find f (−1). __________
b. Find f (2) . __________
c. Find f (3) . __________
d. Find the domain of the function. __________
e. Find the range of the function. __________
Ex. 6) Write the piecewise function given by the graph.
f (x )=⎧
⎨⎪⎪
⎩⎪⎪
x
y
