Algebra 2-Unit 1 Review

A few notes to think about*ask about when to tell an infinity is negative or positive

1.( )=infinity signs always have parentheses!

2. Going right is never negative for infinity other than range because of y being the problem.

Rules for domain

-It goes left to right and is x-values only

-you want to count the whole entire line on the graph.

Rules for range

It goes bottom to top and is the only time you use y related to infinity!

Rules for x-intercepts

-(#,0) use your x axis

-only list numbers on the actual axis line!

Rules for y-intercepts

-(0,#) use your y-axis

-only list numbers on the actual axis line!

Rules for positive

-above x axis

-hand hide bottom half

-only use ( )

-when cut off and another line appears add another parentheses

Rules for negative

-below x axis

-hand hide top half

-only use ( )

-when cut off and another line appears add another parentheses

Rules for increasing

-look left→right going up and finding a line that goes up

-you have to see where the Individual cut-offs are and there can be multiple parentheses sets.

-only ( )

Rules for decreasing

-look left→right going down and a finding a line that goes down

-you have to see where the Individual cut-offs are and there can be multiple parentheses sets.

-only ( )

Rate of change rules

-average rate of change just means slope

-the intervals are always xx never a y featured

-the equation y2-y1 over x2-x1 and then simplify

-the process is always the same

Transformation rules

-the parent functions are linear(line),absolute value(v shape),and quadratic which you can always tell the problem is one when you see x2.

f(x-h) right and f(x+h) left means you flip because there are parentheses

f(x)+k up and f(x)-k down means compression

-f(x) reflection over x-axis

compression and stretching A<1 compress a>1 stretch

Transformation example

part 1-g(x)=3(x+2)²

part 2-g(x)=-(x-5)²+1

part 1

-The three represents the stretch or compress,just say is it greater than 1 that means stretch

-The ² represents the parent function of the quadratic

-The 2 represents going left 2

part 2

-The ² means a quadratic

-The 1 represents going up 1

-The - outside the parentheses represents flipping the x axis

-The -5 means going right 5

Rules for piecewise functions