Understand the equation of a hyperbola
1. Sketch the asymptotes and plot enough points to create and accurate sketch of
y=\frac{1}{x}
2. Find the domain and range of the function:
y=4(\frac{1}{x+5})+7
Understand the equation of a hyperbola
1. Sketch the asymptotes and plot enough points to create and accurate sketch of
y=\frac{1}{x}
2. Find the domain and range of the function:
y=4(\frac{1}{x+5})+7
Examples #2 and #3
{HW_2-28.png} [[cubic|cubic]]cubic
Cubic Functions
{http://i32.tinypic.com/15cg8pt.png}
...
'h' determines the x-coordinate of the inflection point.
'k' determines the y-coordinate of the inflection point. [[exponential|exponential]]exponential
Exponential Functions
f(x)=a(k^x-h)
Hyperbolas, Cubic functions,Exponential functions, and their parent graphs. hyperbolas[[hyperbolas|hyperbolas]]
Hyperbolas
Graphing Equation
...
Examples #2 and #3
{HW_2-28.png} cubic[[cubic|cubic]]
Cubic Functions
{http://i32.tinypic.com/15cg8pt.png}
...
'h' determines the x-coordinate of the inflection point.
'k' determines the y-coordinate of the inflection point. exponential[[exponential|exponential]]
Exponential Functions
f(x)=a(k^x-h)
Hyperbolas, Cubic functions, Exponential functions, and their parent graphs.
hyperbolas
Hyperbolas
Graphing Equation
y=a(\frac{1}{x-h})+k
-'h' is the x asymptote
-'k' is the y asymptote
-'a' is how close/far away the graph is from the point at which the asymptotes intersect
Example #1
{the_wiki.png}
Graphing Form:
y=4(\frac{1}{x+4})+0
'a' is equal to 4
'h' is equal to -4
'k' is equal to 0
Key point =(-4,0) This is where the asymptotes intersect each other.
The 'a' moved the the graph further from the key point.
The 'h' moved the graph 4 points more to the left.
The 'k' didn't move the graph.
Domain = (-oo, -4) and (-4, oo)
Range = (-oo, 0) and (0, oo)
Asymptotes
x=-4 and y=0
To determine the asymptotes you look a the graphing form of the equation. The asymptotes are the h and k in the equation
Examples #2 and #3
{HW_2-28.png}
cubic
Cubic Functions
{http://i32.tinypic.com/15cg8pt.png}
Inflection Point - Where the graph changes from up to down. It's basically the vertex point, but because of the type of equation it is and how the graph looks, it's called an inflection point.
y = a(x-h)^3+k
'a' determines how far away from the inflection point the graph goes.
'h' determines the x-coordinate of the inflection point.
'k' determines the y-coordinate of the inflection point.
exponential
Exponential Functions
f(x)=a(k^x-h)
'k' is the initial value
'a' is the steepness/flatness of the graph
'-h' is the asymptote
This is an example of the parent graph for exponential functions.
{Exponential_Functions.png}