origin symmetry $$f\left(-x\right)=-f\left(x\right)$$

y-axis symmetry $$f\left(-x\right)=f\left(x\right)$$

The number of times a zero occurs in a polynomial

the function crosses through the zero linearly

Multiplicity of 2 ( or any even multiplicity)

The function "bounces" off of the x-axis at the zeros (touches and turns around, does not cross)

Multiplicity of 3 (or any odd after)

The function "wiggles" through the x-axis

Odd degree polynomial with positive leading coefficient

$$\lim_{x\rightarrow-\infty\ }f\left(x\right)=-\infty\ $$ and $$\lim_{x\rightarrow\infty\ }f\left(x\right)=\infty\ $$

Odd degree polynomial with negative leading coefficient

$$\lim_{x\rightarrow-\infty\ }f\left(x\right)=\infty\ $$ and $$\lim_{x\rightarrow\infty\ }f\left(x\right)=-\infty\ $$

Even degree polynomial with negative leading coefficient

$$\lim_{x\rightarrow-\infty\ }f\left(x\right)=-\infty\ $$ and $$\lim_{x\rightarrow\infty\ }f\left(x\right)=-\infty\ $$

Even degree polynomial with positive leading coefficient

$$\lim_{x\rightarrow-\infty\ }f\left(x\right)=\infty\ $$ and $$\lim_{x\rightarrow\infty\ }f\left(x\right)=\infty\ $$

If $$a+bi$$ is a zero of a polynomial then so is $$a-bi$$

Transformations of Functions $$y=af\left(b\left(x-c\right)\right)+d$$ , what is a

vertical dilation by a factor of $$a$$

Transformations of Functions $$y=af\left(b\left(x-c\right)\right)+d$$ , what is b

horizontal dilation by a factor of $$\frac{1}{b}$$

Transformations of Functions $$y=af\left(b\left(x-c\right)\right)+d$$ , what is c

horizontal translation - left or right (opposite of how it looks)

Transformations of Functions $$y=af\left(b\left(x-c\right)\right)+d$$ , what is d

vertical translation - up or down

Linear Function from a table

If both input and output values changes consistently (constant rate of change)

Quadratic Function from a Table

If input changes consistently and the 2nd difference of the output values are constant (linear rate of change)

Cubic Function from a table

If the input changes consistently and the 3rd differences of the output values are constant.

Exponential Function from a table

If the input values change consistently and the output values change proportionately.

Logarithmic function from a table

If input values change proportionately and output values changes consistently.

Vertical Asymptote of a rational function

Set the remaining factors in the denominator equal to 0 $$\lim_{x\rightarrow c}R\left(x\right)=\pm\infty\ $$

Horizontal Asymptote of Rational Functions

Compare the degree of the numerator with the degree of the denominator Bigger on bottom $$y=0$$ (BOB=O) Bigger on top - No Asymptote (BOT=N) Exponents are the same, divide coefficients $$y=\frac{a}{b}$$ EATS=D/C

Slant/Oblique Asymptotes of Rational Functions

Only occurs if the degree on top is EXACTLY one degree bigger than the bottom. Use long division to find (ignore any remainder) and Slant will be in the form of $$y=mx+b$$

Holes of Rational Functions

Will occur when a common factor "canals out" after simplifying the rational expression. Find the location by evaluating the simplified expressions at the "canceled out" x-value.

Arithmetic Sequences (Linear)

Have the same common difference between terms $$a_n=a_k+d\left(n-k\right)$$

Geometric Sequences (Exponential)

Have a common ratio (multiply) between consecutive terms $$g_n=g_k\cdot\left(r\right)^{n-k\ }$$

Exponent Properties: $$x^{\frac{m}{n}}=$$

$$\sqrt[n]{x^m}=\left(\sqrt[n]{x}\right)^m$$

Converting between Exponential and Logarithmic Form

$$b^p=n\ \ \leftrightarrow\ \ \log_b\left(n\right)=p$$

Log with a base 10 - written with no base $$\log\left(x\right)$$

Base $$e$$ $$\ln\left(x\right)$$

AP Precalculus Exam Review Flashcards Flashcards

Student preview

86 questions

Show all answers

1.

FLASHCARD QUESTION

Front

Positive rate of change

Back

Increasing function

2.

FLASHCARD QUESTION

Front

Negative rate of change

Back

Decreasing function

3.

FLASHCARD QUESTION

Front

Rate of change is increasing.

Back

Concave up function

4.

FLASHCARD QUESTION

Front

Rate of change is decreasing

Back

Concave down function

5.

FLASHCARD QUESTION

Front

Point of inflection (POI)

Back

Rate of change changes from increasing to decreasing OR decreasing to increasing

6.

FLASHCARD QUESTION

Front

Average rate of change (AROC)

Back

7.

FLASHCARD QUESTION

Front

Odd function

Back

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