Give at least two ways you can tell from an equation, if you have a function ( without graphing or listing ordered pairs)
What is
No exponent greater than 1, no x in denominator, no root of x, xy not multiplied together
100
True or False
A function is even if for every number x in the domain, -x is also in the domain and f(x) = f(-x)
What is true
100
Give the equation of the cubic parent function and draw it on the board
What is f(x) = x^3
100
Describe a one to one function
What is a function that has no repeating y values
200
state the center and radius of the following circle
(x-2)^2 + (y + 4)^2 = 25
What is
center ( 2, -4) r = 5
200
If I have the graph of a relation, how do I determine if it is
a function
What is if it passes the vertical line test.
200
Odd functions are symmetric with _______________
and even functions are symmetric with ____________.
What is odd - origin and even -y axis
200
Name the parent function and describe the transformation
f(x) = l x - 2l +4
What is absolute value
right two and up 4
200
Technique for determining if a graph is of a one to one function
What is the horizontal line test.
300
To change from the general form to the standard for m of a circle, I use this technique...
What is completing the square.
300
evaluate f(3) if f(x) = 3x^2 + 2x - 4
What is 29
300
Draw a function on the board and label where it is increasing, decreasing, positive and negative
What is ( see board.)
300
I function that has different equations for different values of the domain is called
What is a piecewise function.
300
method for determining if two functions are one to one algebraically
What is if f(g(x)) = g(f(x)) = x
400
Give the following equation in standard form
x^2 + y^2 - 2xy - 4y = 4
and state the center and the radius.
What is (x-1)^2 + (y-2)^2 = 9
center (1,2) radius 3
400
Find the domain of the following function
f(x) = (x^2 - 1)/ (X + 4)
What is
all real numbers except - 4
400
The average rate of change of a function from point a to b equals the slope of _____________________ containing the two points (a f(a)) an (b, f(b)) on its graph.
What is the secant line
400
y = af(x) describes which type of transformation
What is a vertical stretch or compression
400
determine if the following functions are inverses...show work on board
f(x) = 4x - 8 g(x) = .25x + 2
What is yes they are inverses
500
Find the standard form of the circle with center (2,3) and tangent to the y-axis
What is ( x + 3)^2 + (y-1)^2 = 9
500
Find the difference quotient of f
f(x+h) - f(x) if F(x) = 4x + 3
h
What is 4
500
True or false, and if false give an example:
Every function must have an absolute maximum and an absolute minimum.
What is
False...if it increases or decreases there are no extrema
500
f(x) = sqrt x give the equation if the graph is shifter right 3, moves down 4 and is reflected about the x axis
What is y = sqrt (3 - x) - 4
500
Find the domain and range of the following function and its inverse and state the inverse
f(x) = (2x - 3) / (x + 4)
What is
( 3 + 4x)/ ( 2-x) D f(x) and range inverse all real numbers except -4; D inverse and R original all real numbers except 2