Function, Domain & Range
IS THIS RELATION A FUNCTION?
{(1,2), (2,4), (3,6), (4,8), (5,10)}YES
What is equation of average rate of change?
F(b)-F(a)/b-a
TRUE OR FALSE:
For any 1:1 function f(x)=y, a function f^-1(x) is an inverse function if f^-1(y)=x which can also be written as f^-1f(x)=x for all x in domain of f and f^-1
TRUE
WHAT IS AXIS OF SYMMETRY FORMULA?
x=-b/2a
DETERMINE DOMAIN AND RANGE OF THIS RELATION?
{(1,2), (2,4), (3,6), (4,8), (5,10)}
D= {1,2,3,4,5}
R={2,4,6,8,10}
RATE OF CHANGE FOR (hint: leave answer with ln):
f(x)=-ln(x+1) on interval [0,4]
-ln5/4
SOLVE:
2|x-4|+3<2
No solution because LHS is nonegative and RHS is negative.
CAN A QUADRATIC FUNCTION HAVE 3 ZEROS?
NO
FIND DOMAIN FOR:
f(x)=2√x+4
[-4,infinity)
GRAPH, FIND LOCAL EXTREMA & INCREASING and DECREASING INTERVALS:
f(x)=x^3-6x^2-15x+20
Local min: (14,-1352)
Local max: (0, 20)
Increasing: (-infinity, 0)U(14,infinity)
Decreasing: (0,14)
FIND VALUES OF X WHEN f(x)=0:
f(x)=|4x+1|-7
x=1.5 and x=-2
f(x) is a linear function and (3,-2) and (8,1) are points on the line, find the slope. Is this line increasing or decreasing?
m=3/5, function is increasing because m>0.
FIND DOMAIN & RANGE FOR:
f(x)=2/x+1
D=(-infinity,-1)U(-1,infinity)
R=(-infinity,0)U(0,infinity)
TRUE OR FALSE:
f(g(x)) = g(f(x)) for any two functions f and g, why?
FALSE.
FIND INVERSE OF:
f(x)=6x-15
USE QUADRATIC FORMULA TO FIND X:
f(x)=16x^2-8x
1/4
If functions f and g have domains Df and Dg respectively, then the domain of f / g is given by?
The intersection of Df and Dg without the zeros of function g
FIND THE TWO FUNCTIONS THAT MAKE THIS A COMPOSITION:
f(x)=√5-x^2
h(x)=5-x^2 & g(x)=√x
SOLVE:
|1/5x+6|=|3/2x-3|
x=90/13 and x=-30/17
USING QUADRATIC FORMULA TO FIND X:
6+2x^2-3x=8x^2
x=1+/-√17/-4