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

Access all questions and much more by creating a free account

Create resources

Host any resource

Get auto-graded reports

Continue with Google

Continue with Email

Continue with Classlink

Continue with Clever

or continue with

Microsoft

Apple

Others

Already have an account?

Similar Resources on Wayground

54 questions

Historical Events and Concepts in Canada

Flashcard

•

11th Grade

53 questions

G9-U9- WORLD ENGLISHES

Flashcard

•

9th Grade

111 questions

G9-U10-Planet Earth

Flashcard

•

9th Grade - University

52 questions

Phrasal Verbs Flashcards

Flashcard

•

University

74 questions

Civil Engineering Law - Republic Act No. 544

Flashcard

•

KG

70 questions

VOCAB GIẤY 1+2

Flashcard

•

University

66 questions

SP1 Unidad 3: La ropa (Vocabulario)

Flashcard

•

9th - 12th Grade

57 questions

CỤM TRƯỜNG THPT HẢI DƯƠNG

Flashcard

•

12th Grade

Popular Resources on Wayground

8 questions

Spartan Way - Classroom Responsible

Quiz

•

9th - 12th Grade

15 questions

Fractions on a Number Line

Quiz

•

3rd Grade

14 questions

Boundaries & Healthy Relationships

Lesson

•

6th - 8th Grade

20 questions

Equivalent Fractions

Quiz

•

3rd Grade

3 questions

Integrity and Your Health

Lesson

•

6th - 8th Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

9 questions

FOREST Perception

Lesson

•

KG

20 questions

Main Idea and Details

Quiz

•

5th Grade

Discover more resources for Mathematics

14 questions

Making Inferences From Samples

Quiz

•

7th - 12th Grade

16 questions

Properties of Quadrilaterals

Quiz

•

11th Grade

23 questions

8th grade math unit 5B Perfect Squares and Cubes

Quiz

•

6th - 12th Grade

12 questions

Add and Subtract Polynomials

Quiz

•

9th - 12th Grade

10 questions

Quadratic Regression Practice

Quiz

•

7th - 12th Grade

20 questions

Triangle Congruence Statements Quiz

Quiz

•

9th - 12th Grade

20 questions

5.1 Characteristics of Exponential Functions Lesson Check

Quiz

•

9th - 12th Grade

10 questions

Solving two-step equations

Quiz

•

7th - 12th Grade