algebra 2 cc test 1

If the point (-3,5) lies on the graph of y=f(x), then which of the following points must lie on the graph of its inverse?

(5,-3)

Example of interval notation

(5,12] Do not include 5 but do include 12 {x | 5< x <orequalto 12} SET BUILDER

For a function y=h(x) it is know that h(5)=21. Which of the following points must lie on the graph of h(x)?

(5,21)

Determine any values of x that do not lie in the domain of the function f(x)= 3x+2/2x-10

0=2x-10 10=2x x=5 If the denominator is 0, the function is undefined

Ways to represent a function

1) Graphically 2) Table of values 3) Rule- Function notation f(x)=y ex) y=2x+3 and f(x)=2x+3

What are the three parts to a function?

1) Input 2) Relationship/ Rule 3)Output

How do I know if my relationship is a function?

A function relates each input to ONE AND ONLY ONE output.

What is a function?

A rule that RELATES how one quantity depends on other quantities. (A function relates an INPUT to an OUTPUT)

What are the relative maximums and minimums? (state x coords)

ALL turning points NOT starting and end points

Roster form

All in inputs in brackets and all the outputs in brackets

What happens to the domain and range of an INVERSE function?

Domain becomes range of other function Range becomes domain of other function

Find f(2) when f(x)=3x in English

Find y when x=2, for y=3x

What are inverse functions?

Functions that are symmetrical over the line y=x

A function f(x) is odd if

GRAPHICALLY: f(x) is symmetric with respect to the origin (rotation around origin) ALGEBRAICALLY: f(x)=y and f(-x)=-y -f(x)=f(-x)

A function f(x) is even if

GRAPHICALLY: f(x) is symmetric with respect to the y-axis (line reflection over x=0) ALGEBRAICALLY: f(x)=y and f(-x)=y... f(x)=f(-x)

What does "find all values of x" mean?

INPUTS

Inverse function notation

If a function y=f(x) has ab inverse that is also a function we represent it as y=f^-1(x)

When will a function have an inverse that is also a function?

If the inverse has one and only one output for each input *Passes horizontal line test

Over the interval ___ is f(x) increasing or decreasing? How can you tell?

Increasing- the y values are increasing Decreasing- the y values are decreasing

How many points should you use to get accurate info?

MORE THAN 1

Are there ary other values other than 4 (in 2x+1/x-4) that are not in the domain of f?

No because no other number subtracted from 4 will give you 0.

What does "evaluate" mean?

OUTPUTS

When does the abs max/ min not exist?

On a graph with arrow (up for max, down for min)

The function y=f(x) has an inverse function y+f^-1(x)...

SWITCH X AND Y

What is the domain of a function?

Set of all inputs (x-values) for which the function is defined

What is the range of a function?

Set of all outputs (y-values) that come from the function's domain

What are the absolute maximum and minimums?

The abs. max/min is __ at x=___ The abs. max and min are the highest and the lowest points on the graph (CAN BE END POINTS)

Why does the calculator say ERROR?

The difference of the numbers = 0 and any fraction where 0 is the denominator is an undefined output.

What is an odd function?

The inputs x and -x have negated outputs. (DIFF sign, SAME value)

What is an even function?

The inputs x and -x have the exact same output y.

What special features on a graph does the set of x-values that solve f(x)=0 correspond to?

The roots

What special feature on a graph does f(0) always correspond to?

The y-intercept

What happens to the x and y values in an INVERSE function?

They swap

Which of the following values of x "would not be in the domain" of the function...

Whichever value makes the denominator equal 0.

Give the interval over which f(x)>0.

X < __ and X > __ Values above the x axis

What makes a function undefined?

X/0

What happens to the x and y intercepts of an INVERSE function?

XINT becomes YINT of other function YINT becomes XINT of other function

Interval notation

[ ] - use a square bracket to INCLUDE the end value ( )- use a round bracket to EXCLUDE the end value **INFINITY ALWAYS gets a soft bracket

f(x)> 0

above x-axis!!!!!!! root 1 < x < root 2 (NOT LESS THAN OR EQUAL TO)

Minimum and maximum x-values are the

domain

Function Notation

f(x) =

A second function g(x) is defined using the rule g(x)=3-2f(x). Evaluate g(0) using this rule.

g(x)=3-2f(x) g(0)=3-2f(0) g(0)=3-2(-2) g(0)=3+4 g(0)=7 USE GRAPH FOR F(X) VAL

If the input is repeated the relationship...

is NOT a function

Minimum and maximum y-values are the

range

The f(x) notation is another way of representing...

the y-value in a function **f(x)=y

Which of the following values if x would not be in the domain of the function y=SQROOTOFx+4?

x+4>= 0 x>= -4 DOMAIN MUST BE GREATER THAN OR EQUAL TO =4

Set-builder notation

{x | x > 0} { = the set of x= all x | = such that x>0 = x is greater than 0

Which of the following would represent the domain of the function y=[SQUAREROOTOF]6-2x?

{x|x<OR=TO3} Y CAN EQUAL SQROOTOF 0