Properties of Functions
Graphing
Linear Equations
Polynomials
Inequalities
100
Is the point (-1,2) on the graph of
f(x)=-3x^2+5x?
No,
f(-1)=-8
100
Draw a quick sketch of the cube root function.
Domain:
(-oo,oo)
Range:
(-oo,oo)
100
What is the slope of the equation
g(x)=2x-17?
m=2
100
What do you call the graph of a quadratic function?
A parabola.
100
Solve the inequality
(x-5)^2(x+2)<0
(-oo,-2)
200
The graph of a function
y=f(x)
can have more than one of what type of intercept?
a) y-intercept
b) x-intercept
c) both
d) neither
a) x-intercepts
These are also called the zeros or roots of the function.
200
Draw a quick sketch of the reciprocal function.
Domain:
(-oo,0)uu(0,oo)
Range:
(-oo,0)uu(0,oo)
200
What is the average rate of change of the line
v(t)=-1/3t+1?
The average rate of change is
-1/3
200
Given the function
f(x)=-3(x-1)^2+2
Does it open up or down?
Down
200
Solve the inequality
x^3+8x^2>=0
[-8,oo)
300
Give the absolute maximum and absolute minimum of the graph if they exist.
There is no absolute max or min.
300
Graph the function:
g(x)=(x-1)^3
Domain:
(-oo,oo)
Range:
(-oo,oo)
300
What is the y-intercept of the line
h(x)=-pix+42?
(0,42)
300
What is the
a) vertex
b) x-intercepts
c) y-intercept
d) Domain and Range
d) axis of symmetry of the function.
g(x)=3x^2+6x?
Vertex: (-1,-3)
x-intercepts: (-2,0) and (0,0)
y-intercept: (0,0)
Domain:
(-oo,oo)
Range:
[-3,oo)
Axis of Symmetry:
x=-1
300
Solve the inequality
(x-3)/(x+1)>0
(-oo,-1)uu(3,oo)
400
Answer the following questions about the graph:
a) What is the absolute maximum if it exists?
b) Where is a local maximum if it exists?
c) Where is the absolute minimum if it exists?
d) What is a local minimum if it exists?
a) 33
b) -2
c) -4
d) Does not exist
400
a) Over what interval(s) is the function increasing?
b) Over what interval(s) is the function decreasing?
c) Over what interval(s) is the function constant?
a)
(-4,-2),(2/3,3)
b)
(-2,2/3)
c) None
400
What can you say in general about the slopes of a line that are:
a) Increasing
b) Decreasing
c) Horizontal
d) Vertical
a) Positive
b) Negative
c) Zero
d) Undefined
400
Solve the inequality
(x+2)/(x-4)>-1
(4,oo)
500
Given the function below what is the average rate of change from 2 to 5 and what is the name of line this would be the slope of?
g(x)=x^2-2x+3
Average rate of change = 5
This is the slope of the secant line between the points (2,3) and (5,18).
500
a) Graph
b)Continuous or discontinuous?
c) Domain?
d) Range?
g(x)={(abs(x+3)-1,if -7<=x<0),(sqrt(x)+2, if x>=0):}
Continuous
Domain:
[-7,oo)
Range:
[-1,oo)
500
A cell phone company offers an international plan by charging $30 per month and $0.50 per minute.
a) Write the a linear model that relates C, in dollars, of talking x minutes.
b) What is the cost for talking 105 minutes?
a)
C(x)=0.50x+30
b)
C(105)=82.5, $82.50
500
A ball is thrown vertically upward with an initial velocity of 96 feet per second. The distance s (in feet) of the ball from the ground after t seconds is
s(t)=96t-16t^2
At what time t will the ball strike ground?
6 seconds