Is the following a function? Explain.
Yes, it passes the vertical line test.
What type of symmetry does this graph have?
Origin Symmetry
What are the three types of discontinuity in a graph?
Infinite, Jump. Removable
What are all the types of extrema on a graph?
Relative Maximum
Relative Minimum
Absolute Maximum
Absolute Minimum
Name 3 Parent Functions that were new this year.
Greatest Integer Function, Reciprocal, Cubic
What are the three cases for domain restrictions?
1. 1/x ; x \ne0
2. sqrtx; x>=0
3. 1/sqrtx; x>0
Write set-builder and interval notation for the following, if possible.
x<=4
Interval:
(-oo, 4]
Set-Builder:
{x|x<=4;x inR}
If a function is odd, it has symmetry about the _____.
Origin
Is the function below continuous?
Yes, it is continuous.
Find and classify the relative minimum of this graph.
What are the anchor points of the square root function?
(0,0) (1,1) (4,2) optional: (9,3)
Find f(g(x)) if
g(x)=x+1
and
f(x)= 2x^2 +5x
f(g(x))=2x^2+9x+7
Write the following in set-builder and interval notation, if possible.
{......3,4,5,6}
Set Builder:
{x|x<=6; x inZ }
Interval : Not Possible
What is the domain of the function below.
Domain: All Real Numbers
For the graph below, identify the location and type of each discontinuity.
Jump Discontinuity at x=1.
On what intervals is this graph increasing? Decreasing?
Decreasing:
(0,2)
Increasing :
(-oo,0)U(2,oo)
Sketch a graph of the following:
f(x)= 1/(x+2)-3
Come up with functions f(x) and g(x) such that f(g(x))=h(x) if
h(x)=(x^2 +3)/(x^2-1)
g(x)= x^2 +3
f(x)= x/x-4
OR
g(x)= x^2 -1
f(x)= x+4/x
State the domain of the following function.
sqrt(x-2)/(x^2+5x+6)
Domain:
[2, oo)
{x|x>=2; x inR}
What are the rules for finding if a function is even and odd? *HINT* they use f(x)=
Even: f(x)=f(-x)
Odd: -f(x)=f(-x)
OR f(x)=-f(-x)
What is the end behavior of the graph below?
lim/(x->oo)f(x)=1 lim/(x->-oo)f(x)=1
Classify all the extrema of graph below.
Absolute Min. of -3 at x=2,-2
Relative Max of 1 at x=0
Sketch a graph of the greatest integer function.
Find f(x)*g(x) and the domain restrictions.
f(x)=sqrt(x-5)
g(x)=1/(x^2+6x+8
sqrt(x-5)/(x^2+6x+8)
{x|x>=5;x inR}
[5,oo)
State the domain of the function.
2/sqrt(4x^2-16)
Domain:
(-oo,-2)U(2,oo)
What would the y-intercept of the function below be?
(2x+1)/(x^2-4)
y-intercept:
(0, -1/4)
Determine between which consecutive integers the real zeros of each function are located on the given interval.
f(x)=-2x^3+9x ; [-3,1]
There are zero's on the interval (-3,-2) and at x=0.
Find the average rate of change of the function on the interval below.
f(x)=1/2x^2-4x+2; [-2,4]
-3
Create an equation for the graph below.
f(x)=2sqrt(x+4)
Find the difference quotient of
f(x)=2x^2+3x
4x+2h+3