Definitions I
a rule of assignment which assigns to each possible input at most one output
Function
sum of constants times nonnegative powers of x
Ex: f(x) = ax2+bx+c; a,b,c are constants
Polynomial
What does the imaginary number i equal?
The square root of negative one (-1)
given:
f(x) = -3x2+2
find:
f(2), f(0)
f(2) = -3(2)2+2 = -3*4+2 = -12+2 = -10
f(0) = -3(0)2+2 = -3*0+2 = 2
In interval notation, find the range of the following:
f(x) = x2 - x - 6
(-inf, inf)
set of all inputs which produce valid outputs under f
Domain
names for where the graph of a function crosses the x and y axes
X- and Y- intercepts
On the unit circle, what coordinate values do cosine and sine represent?
cos : x
sin: y
In interval notation, what is the domain of the following:
f(x) = 1 / sqrt(1 - x2)
Domain: (-1,1)
Sketch the graph of the following from x = -5 to x = 5:
f(x) = x2 - 25
See tutor graph
all outputs f has for inputs in its domain
Range
p(x) / q(x)
where p and q are polynomials
Rational Functions
What do degrees and radians measure?
angles
Expand the following:
f(x) = (x - 3)(x2 + 2x - 3)
f(x) = x3 - x2 - 9x + 9
Rewrite the following as a rational function involving negative exponents:
f(x) = (x4 + x3 - 2x + 3) / x3
f(x) = x + 1 - 2x-2 + 3x-3
set of all points in the form (input, output) or (x, f(x))
Graph of a function
Rational functions with roots
Algebraic functions
How do you convert from degrees to radians?
Multiply the degrees by pi, divide the product by 180
Using polynomial factorization, find the roots of the following:
f(x) = x2 + 2x - 3
x = -3, 1
Rewrite the following using radicals:
f(x) = x2/3 + x3/5
See tutor solution
f(x) = xn, where n is an integer
Power function
What is the quadratic formula?
x = [(-b) +/- sqrt(b2-4ac)] / 2a
"X is equal to negative b plus or minus the square root of b squared minus 4 times a times c, all divided by 2 times a"
How do you convert from radians to degrees?
Multiply the radians by 180, divide the product by pi
Using the quadratic formula, find the roots of the following:
f(x) = x2 - 2x - 8
x = -2, 4
Using the quadratic formula, find the roots of the following:
f(x) = (1/4)x2 + 4x + 25
x = -8 + 3i, -8 - 3i