# precalculus regents review

##### SETS

Midpoint Formula

Distance Formula

Equation of a Circle

Slope Equation

Midpoint Formula

Distance Formula

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

Midpoint Formula

Distance Formula

Equation of a Circle

Slope Equation

Midpoint Formula

Distance Formula

What is e to the tenth place?

Simplify: log(a + b)

Simplify: log(a - b)

What is log(ab) expanded?

2.7

Can't be done!... log(a + b)

Can't be done!... log(a - b)

log(a) + log(b)

What is e to the tenth place?

2.7

Simplify: log(a + b)

Can't be done!... log(a + b)

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…

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

linear function

direct variation

quadratic

reflection over x-axis (y-coordinates b…

f(x)=mx+b

f(x)=mx

f(x)=ax²+bx+c or f(x)=a(x-h)² +k

-f(x)

linear function

f(x)=mx+b

direct variation

f(x)=mx

Reference

1/2

√2/2

√3/2

A__________ angle is between 0º and 90º.

sin(30º) is__________.

sin(45º) is__________.

sin(60º) is__________.

Reference

A__________ angle is between 0º and 90º.

1/2

sin(30º) is__________.

sin 0

sin(π/6)

sin(π/4)

sin(π/3)

0

1/2

√2/2

√(3)/2

sin 0

0

sin(π/6)

1/2

Difference Quotient Formula

Exponential Function

Natural Exponential Function

Compound Intrest Formula

[f(x+h)-f(x)]/h

f(x)=a^x; a>0, a≠1

f(x)=e^x

A=P(1+r/n)^(nt)

Difference Quotient Formula

[f(x+h)-f(x)]/h

Exponential Function

f(x)=a^x; a>0, a≠1

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…

Distance Formula

Equation of a Circle

Slope Equation

Point-Slope Formula

Distance Formula

Equation of a Circle

Domain of y=sin⁻¹x

Range of y=sin⁻¹x

Domain of y=cos⁻¹x

Range of y=cos⁻¹x

-1 ≤ x ≤ 1

-π/2 ≤ y ≤ π/2

-1 ≤ x ≤ 1

0 ≤ y ≤ π

Domain of y=sin⁻¹x

-1 ≤ x ≤ 1

Range of y=sin⁻¹x

-π/2 ≤ y ≤ π/2

Algebra 2

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…

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…

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(…

Biology

Autotroph

Organelle

heterotroph

meiosis

An organism that makes its own food

A tiny cell structure that carries out a specific function wit…

An organism that obtains organic food molecules by eating othe…

Cell division that produces reproductive cells in sexually rep…

Autotroph

An organism that makes its own food

Organelle

A tiny cell structure that carries out a specific function wit…

horizontal asymptote when the degree of…

horizontal asymptote when the degree of…

horizontal asymptote if the degree of n…

vertical asymptote

divide the coefficients of the highest degree terms

y=0

found by dividing the numerator by the denominator

found by setting the denominator equal to zero

horizontal asymptote when the degree of…

divide the coefficients of the highest degree terms

horizontal asymptote when the degree of…

y=0

slope-intercept form

point-slope form

cos2x+sin2x

tan2x+1

y=mx+b

y-y1=m(x-x1)

1

sec2x

slope-intercept form

y=mx+b

point-slope form

y-y1=m(x-x1)

a^2 = (law of cos)

CosA = (law of cos)

Even function test

Odd function test

b^2 + c^2 - 2bc cos A

(b^2+c^2-a^2)/(2bc)

f(x) = f(-x)

f(x) = -f(-x)

a^2 = (law of cos)

b^2 + c^2 - 2bc cos A

CosA = (law of cos)

(b^2+c^2-a^2)/(2bc)

composite function

decreasing

domain

even function

f(g(x))

f(-x)=f(x)

composite function

f(g(x))

decreasing

Midpoint Formula

Distance Formula

Equation of a Circle

Slope Equation

Midpoint Formula

Distance Formula

definition of (a,b)

definition of [a,b]

definition of [a,b)

definition of (a,b]

a<x<b

a≤x≤b

a≤x<b

a<x≤b

definition of (a,b)

a<x<b

definition of [a,b]

a≤x≤b

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…

In quadrant 4, is y positive or negative

In quadrant 3 is y positive or negative

In quadrant 3 is x positive or negative

In quadrant 2 is x positive or negative

negative

negative

negative

positive

In quadrant 4, is y positive or negative

negative

In quadrant 3 is y positive or negative

negative