Functions
Is y=5x+1 a function?
Yes.
Domain is associated with what variable?
x, independent
When a function goes from decreasing to increasing, we call the turning point a _______.
Minimum
In which direction is f(x) translated when its transformation g(x) = f(x-3)?
Right
Is y=x2+1 a function?
Yes.
Range is associated with what variable?
y, dependent
When a function goes from increasing to decreasing, we call the turning point a _______.
Maximum
In which direction is f(x) translated when its transformation g(x) = f(x)+2?
Up
Is {(6,10)(−7,3)(0,4)(6,−4)} a function?
Not a function.
What is the range of the function f(x)=x^2 ?
[0, ∞)
What is the formula for rate of change?
A([a,b]) = (f(b)-f(a))/(b-a),
or R = (y_2 - y_1)/(x_2 - x_1)
How is -f(x) different from f(x)?
It is reflected vertically
Is x^2+y^2=4 a function?
Not a function.
Daily Double: What is the domain of the function f(x)=|x-1|?
All Real Numbers, (-∞, ∞)
Rate of change of f(x) = x on the interval [2,3].
1
Write the transformation that moves f(x) = x^2 down 3 units and right 4 units.
g(x) = f(x-4)-3, or
g(x) = (x-4)^2 - 2
a relation for which each value from the set the first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pair.
What is a function?
When do we use "(" and ")" to describe intervals?
When the beginning or endpoints of the interval are not included on the interval.
Rate of change of y = x^3 - x^2 + 16 on the interval [-3,1].
9
What do a,b,c,d represent in the general transformation g(x) = a*f(b(x-c))+d
parameters, or:
a - expand/compress vertically
b - expand/compress horizontally
c - translate left/right
d - translate up/down