# precalculus regents review

##### SETS

find the midpoint between to points

find the distance between two points

x > 0 and y > 0 describes which quadran…

x < 0 and y > 0 describes which quadran…

1. x-coordinate → add the x-values & divide by 2... 2. y-coordina…

1. subtract the x-values & square that... 2. subtract the y-value…

Quadrant I

Quadrant II

find the midpoint between to points

1. x-coordinate → add the x-values & divide by 2... 2. y-coordina…

find the distance between two points

1. subtract the x-values & square that... 2. subtract the y-value…

exponential function

exponential growth

exponential decay

logarithmic function

f(x) = ab^x, where a and b are real numbers with a ≠ 0, b>0, a…

f(x)=ab^x, where b > 1

f(x)=ab^x, where 0 < b < 1

f(x)=logbX, where b≠1 and b>0

exponential function

f(x) = ab^x, where a and b are real numbers with a ≠ 0, b>0, a…

exponential growth

f(x)=ab^x, where b > 1

Not a Function

as x→∞, f(x)→-∞, ... as x→-∞, f(x)→∞

(-∞, -4)U[10, ∞)

(-1.45, -6.76)

Function or Not?

Describe the end behavior of g(x) = -4x³-5x+1

Describe the set of numbers below using interval notation:... x <…

Determine the relative minimum point of the following function…

Not a Function

Function or Not?

as x→∞, f(x)→-∞, ... as x→-∞, f(x)→∞

Describe the end behavior of g(x) = -4x³-5x+1

Leading Coefficient

Degree

Zero Function

Constant Function

The number in front of the X of the highest degree ... (ex.) (4)x…

The highest exponent in a polynomial determining the number of…

A polynomial with no degree and a slop of zero... {f(x)= 0 }

A polynomial with a constant and no degree ... {f(x)= a}

Leading Coefficient

The number in front of the X of the highest degree ... (ex.) (4)x…

Degree

The highest exponent in a polynomial determining the number of…

A hyperbola with a positive y term opens

A hyperbola with a positive x term opens

The y value of the vertex of an upwards…

The x value of the vertex of a sideways…

Up

Sideways

The square root of b

The square root of a

A hyperbola with a positive y term opens

Up

A hyperbola with a positive x term opens

Sideways

primary sources

geographer

archaeologist

economist

• are from the events they are about... • diaries, letters, films…

• studies how landforms, water, climate, and location affect p…

• studies artifacts (human-made objects)

• studies how goods and resources are used

primary sources

• are from the events they are about... • diaries, letters, films…

geographer

• studies how landforms, water, climate, and location affect p…

Distance

Displacement

Slope of d vs. t graph

Slope of v vs. t graph

The length of the path traveled by an object.

The length and direction of a straight line from an object's i…

Velocity

Acceleration

Distance

The length of the path traveled by an object.

Displacement

The length and direction of a straight line from an object's i…

Homeostasis

Metabolism

Organic Molecules

Organelle

The ability of an organism to maintain internal stability

the sum of all the chemical reactions that occur within the ce…

Contain both Carbon and Hydrogen

small parts that make up a cell (each has at least one specifi…

Homeostasis

The ability of an organism to maintain internal stability

Metabolism

the sum of all the chemical reactions that occur within the ce…

amp=2... per=4π... PS=2π

amp=2... per=π... PS=π

amp=2... per=π... PS=1

f(x)=cos 4x

Find the amplitude, period, and phase shift of: ... f(x) = 2sin ½…

Find the amplitude, period, and phase shift of: ... f(x) = -2cos(…

Find the amplitude, period, and phase shift of: ... f(x) = -2sin(…

What is the equation of the graph?

amp=2... per=4π... PS=2π

Find the amplitude, period, and phase shift of: ... f(x) = 2sin ½…

amp=2... per=π... PS=π

Find the amplitude, period, and phase shift of: ... f(x) = -2cos(…

Rational Number

Irrational Number

Quadratic Formula

Factoring Cubes

-any number that is a real number that can be written ass a te…

-real number that cannot be written as a terminating or repeat…

-b±[√b²-4ac]/2a

a^3+b^3=(a+b) (a^2-ab+b^2)... -if it is A^3-B^3 then change to (a…

Rational Number

-any number that is a real number that can be written ass a te…

Irrational Number

-real number that cannot be written as a terminating or repeat…

Find a function where y is a function o…

Find an equation of a line perpendicula…

tan

cot

1. Get y all by itself... 2. See if you can tell there's going t…

Convert equation to slope intercpt form... Perpendicular lines h…

sin/cos

cos/sin

Find a function where y is a function o…

1. Get y all by itself... 2. See if you can tell there's going t…

Find an equation of a line perpendicula…

Convert equation to slope intercpt form... Perpendicular lines h…

Midline

Amplitude

Period

sin(θ)

The average value (in the context of sinusoidal functions).

The distance that the graph of a sinusoidal function deviates…

The shortest distance along the horizontal axis over which the…

The vertical coordinate of the point of intersection of the un…

Midline

The average value (in the context of sinusoidal functions).

Amplitude

The distance that the graph of a sinusoidal function deviates…

2x + 9

Even Degree / Positive Leading Coeffici…

Infinite Discontinuity

x-5

f(x) = x + 9 and g(x) = 2x ... find f[g(x)]

State the Degree and Leading Coefficient

This type of discontinuity is where vertical asymptotes are

2x + 9

f(x) = x + 9 and g(x) = 2x ... find f[g(x)]

Even Degree / Positive Leading Coeffici…

State the Degree and Leading Coefficient