1a - Function Features
1b - Piecewise Functions
1c - Transformations
1d - Combinations and Compositions
1e - Inverses
100
What is the range of this function?
[1, oo)
100
True or False: For a piecewise function, we would graph an open dot at x=-2 for a piecewise function with the following domain restriction:
x<=-2
False!
100
What is the name of the parent function for the following graph of g(x):
Square Root (Radical) Function:
f(x) = sqrtx
100
Given f(x)=x^2-x +3 and
g(x)=2x-5 find f+g.
f+g=x^2+x-2
100
Select all that are true:
A. Inverse functions are a reflection across the x-axis.
B. If the point (-1,2) lies on f(x) then the point (2,-1) must also lie on
f^-1(x) .
B only.
200
On which interval(s) is the function increasing?
(3,4),(5,00)
200
Given the piecewise function f(x), find f(5).
f(5)=13
200
Describe the transformation that occured.
g(x)=-f[3(x-1)]+2
Reflection over the x-axis, horizontal shrink by 1/3, horizontal translation right 1, vertical translation up 2.
200
Given f(x)=x^2-x +3 and
g(x)=2x-5 find
f/g.
f/g=(x^2-x+3)/(2x-5), for x !=5/2
200
Two functions, f(x) and g(x), are inverses of each other if ___________________.
fcircg=gcircf=x
300
Given the location of all relative maximums of the function f(x).
(4,2)
300
Given the piecewise function f(x), find f(-10).
f(-10)=104
300
Give the ordered pair rule for the following transformation.
g(x)=-3f[-1/2(x-1)]+2
(x,y)->(-2x+1,-3y+2)
300
Given f(x)=x^2-x +3 and
g(x)=2x-5 evaluate
(fcircf)(-1) .
(fcircf)(-1)=23
300
Find the inverse of
f(x)=-2sqrt(x+1) .
f^-1(x)=(x/-2)^2-1,x<=0
400
Is this function odd, even or neither?
Neither
400
True or False? Given the piecewise function f(x), at x=0 the two piecewise functions that share that domain will connect at the same point.
False!
400
Write the function g(x) that matches the graph.
g(x) = -sqrt(x-2)-1
400
Given f(x)=x^2-x +3 and
g(x)=2x-5 find
(gcircf)(x)
gcircf=2x^2-2x+1
400
Find the inverse of
f(x)=x^4/3-2 .
f^-1(x)=root(4)(3(x+2)
500
You are completing the "negative x test" and you determine that f(x) = f(-x). Does that make the function f(x) odd, even or neither?
EVEN
500
A piecewise function is said to be "continuous" if there are no breaks or gaps in the line that is formed.
Is this piecewise function continuous?
Yes!
At x=1 both lines meet at (1,5).
At x=3 both lines meet at (3,1).
500
Give the table of points that would graph the quadratic function
g(x) = -2f[-(x+1)] + 2
500
A manufacturing firm can model the number of units produced N(x) based on x hours the firm is operating with
N(x)=25x, 0<=x<=12 , The cost of production is dependent on the number of N units produced in a day with
C(N)=2N+1500
. Find and interpret
(CcircN)(8).
(CcircN)(x)=50x+1500
At 8 hours of operation, the cost of production is $1,900.
500
In order to consider if g(x) is the inverse of
f(x)=3x^3-5 what type of function would g(x) have to be?
A cubed root function g(x)=
root(3)x+-_