Domain and Range
Increasing/ Decreasing
AROC
Evaluate
100
What is the domain of
f(x)=sqrt(3-x)
x<=3
100
Where is the function
f(x)=3|x+1|
decreasing?
Decreasing:
(-oo,-1)
100
The average rate of change
(f(b)-f(a))/(b-a)
calculates the ___________ of the __________ line that passes through the points __________.
The average rate of change calculates the slope of the secant line that passes through the points a and b.
100
Find f(-2) if
f(x)=-x^2-3x+2
f(-2)=4
200
What is the range of
g(x)=sqrt(-x)+1
y>=1
200
On what intervals is
f(x)=-1/x
decreasing?
It never decreases in its domain.
200
The table below gives the temperature (in °F) of a bowl of soup t minutes after it was set on the table.
During which interval did the soup cool off more quickly?
On the first interval.
200
f is a one-to-one function. Find
f^-1(f^-1(0))/([f(3)]^2)*f^-1(2)
3
300
What is the domain and range of
f(x)=-|x-3|-1
Domain:
R
Range:
(-oo,-1]
300
On what interval is
f(x)=x^(1/3)
increasing?
Increasing:
(-oo,oo)
300
Which of the following functions is increasing at a faster rate on the interval [1,2]?
f(x)=2x^2-3x+1
g(x)=2(x-1)^4
Explain your answer.
f is growing faster than g on [1,2]
300
Selected values for f and g are given in the following table:
If
h(x)=f(x)g(x)
find the net change of h on the interval [1,3].
-2
400
What is the domain of
h(x)=1/(sqrtx-2)
in interval notation?
[0,4)∪(4,oo)
400
Where is the following function decreasing?
Decreasing:
(-2,0) and (2,oo)
400
The secant line that passes through the points [a,b] on the function g(x) is parallel to the line y+x=3. What is the average rate of change of g(x) on [a,b]?
-1
400
f and g are defined as follows:
Find
(f∘g)(-3)
(f∘g)(-3)=-1/2
500
What is the domain and range of
g(x)=1/(x^2-2x+1)-2
Domain:
{x:x≠1}
Range:
{y:y>2}
500
State where
f(x)=cos x
is increasing and decreasing on
[0,2pi]
Decreasing:
(0,pi)
Increasing:
(pi,2pi)
500
If
f(x)=|2x|
what is the average rate of change of f on the interval [-1232425.997,-800]?
The AROC on [-1232425.997,-800] is -2.
500
Find
(f(a+h)-f(a))/h
if
f(x)=3x^2+2
(f(a+h)-f(a))/h=6a+3h