Functions
What test do we use to determine if a graph shows a function or not?
Vertical line test
Describe all transformations from the parent graph:
f(x)=x2+8
Vertical translation of the quadratic function up 8.
Rewrite the expression in exponential form:
log2(32)=5
25=32
sin(90 degrees)
1
Factor:
6k2+9k
3k(2k+3)
Let f(x)=2x2-5x+1. Evaluate f(3).
4
Write the function of the absolute value function translated to the left 7.
f(x)=|x+7|
Simplify:
(2a3b5c)x(5a-2b6c2)
10ab11c3
Convert 45 degrees to radians.
pi/4
Factor:
x2-7x-18
(x-9)(x+2)
Why does f(x)=|x| not have an inverse?
Because it doesn't pass the horizontal line test.
What is the domain of
f(x)=sqrt(4x-8)
in interval notation?
[2,infinity)
Solve for x:
log3(x)=5
x=35=243
What trig function is a ratio of opposite over adjacent?
Tangent
Factor:
5p2-p-18
(5p+9)(p-2)
Find the inverse of
f(x)=log2(x+5)-3
f-1(x)=2x+3-5
Sketch a graph of
f(x)=-sqrt(x)-1
Starts at (0,-1); vertical reflection of sqrt(x)
Solve for x:
3x=9x+5
x=-10
tan-1(sqrt(3))
60 degrees or pi/3
Factor:
3b3-5b2+2b
b(3b-2)(b-1)
Let f(x)=x2-x.
Find f(x+h)-f(x).
2xh+h2-h
Describe all transformations from the parent graph:
f(x)=-3|x-5|-6
vertical reflection, vertical stretch by factor of 3, right 5, down 6
Solve for x:
5e2x+4-8=0
x=(1/2)(ln(8/5)-4)
What is the maximum height that a 20 foot ladder can reach safely if we follow the suggestion that the ladder should not make an angle greater than 75 degrees with the ground?
19.32 feet
Factor:
2y3-3y2+18y-27
(2y-3)(y2+9)