Algebra 2 Honors - Midterm

Multiplying or diving by a negative (inequalities)

Switch the inequality

And (inequality)

Intersections of solutions

Or (inequalities)

Union of solutions

Quadratic inequalities

1) Set the equation equal to zero

2) Factor to find the zeros of the graph

3) Graph

4) Answer with graph

Absolute Value Inequalities

1) Isolate the absolute value

• A negative number cant be greater than the isolated absolute value

2) Set up two inequalities

Quadratic function

f(x)=x²

liner function

f(x)= x

absolute value

f(x)= |x|

Cubic function

f(x)= x³

Square root function

f(x)= \|x|

cubic root function

f(x) = ³\|x|

exponential

f(x)= b^x

reciprocal

f(x)= 1/x

Inside transformations

X transformations (crazy x, horizontal)

Outside transformations

Y transformations (vertical)

Limits

End behavior of a line (as x approaches … y approaches…)

Polynomial end behavior

Use leading coefficient and degree to find end behavior

Rational functions end behavior

Use Bobo, botn, eats dc, to find end behavior

Bobo

Bigger on bottom, horizontal asymptote equals 0

Botn

Bigger on top, no horizontal asymptote

Eats Dc

Exponents are the same, divide coefficients to find horizontal asyptote

Finding limits algebraically

1) substitution (if 0/0, don’t know the limit)

2) factoring (0/#, lim is zero, #/0, lim does not exist)

Continuity test

1) find the function value

2) find the limit

3) function value and limit must equal to each other, making the function continuous at x=#