AP Pre-Calculus Study Guide

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What is the slope intercept formula?

y = mx + b

What is the point-slope formula?

y-y₀ = m(x-x_o)

What is the Law of Zero Exponent?

a⁰=1

What is the Law of Power of a Power?

(a^m)ⁿ= a^mn

What is the Power of a Product?

(ab)^m=a^mb^m

What is theLaw of Power of Quotient?

(a/b)^m=a^m/b^m

What is the Law of Negative Exponent?

a^-m=(1/a^m)

What is average rate of change formula?

f(b)-f(a)/b-a

In a rational function, when the leading term degree of the denominator is greater than the numerator, what is the horizontal asymptote?

y=0

In a polynomial function, when the leading term degree of the numerator equals the denominator, what is the horizontal asymptote?

y=a/b

where a is the leading coefficient of the numerator, and b is the leading coefficient of the denominator

In a rational function, when the leading term degree of the numerator is greater than the denominator, what is the horizontal asymptote?

Similar to the quotient of the two polynomials without the remainder.

In a rational function, when the leading term degree of the denominator is greater than the numerator, what is the end behavior defined in liminal notation?

lim f(x) = 0 lim f(x) = 0

x—> -oo x—> oo

In a polynomial function, when the leading term degree of the numerator equals the denominator, what is its end behavior defined by liminal notation?

lim f(x) = a/b lim f(x) = a/b

x—> -oo x—> oo

-Where a is the leading coefficient of the numerator and b is the leading coefficient of the denominator

In a rational function, when the leading term degree of the numerator is greater than the denominator, what is its end behavior in liminal notation?

The end behavior is similar to the quotient of the two polynomials without the remiander

When is a vertical asymptote present?

When the denominator equals zero, but the numerator does not equal zero.

When a polynomial function has a positive sign and even degree, what is its end behavior?

lim p(x) = oo lim p(x) = oo

x —> oo x —> -oo

When a polynomial function has a negative sign and even degree, what is its end behavior?

lim p(x) = -oo lim p(x) = -oo

x —> oo x —> -oo

When a polynomial function has a positive sign and odd degree, what is its end behavior?

lim p(x) = oo lim p(x) =-oo

x —> oo x —> -oo

When a polynomial function has a negative sign and odd degree, what is its end behavior

lim p(x) = -oo lim p(x) = oo

x —> oo x —> -oo

Product property of logs

log_b (x * y) = log_bx + log_by

Quotient property of logs

log_bx/log_by = log_bx - log_by

Power property of logs

log_bxⁿ= n log_bx

Change of base property

log_bx= log_ax / log_ab

Secant

1/cos x

Cosecant

1 / sin x

Cotangent

1 / tan x

Root property

b^1/k= k square root of b.

K is a natural number

When is a hole present in a polynomial?

when multiplicity of the real zero in the numerator greater than or equal to the multiplicity of the denominator