AP Precalculus UNIT 1 Review: Polynomial and Rational Functions (Reteaching Test Practice Problems)

Unit 1: Polynomial and Rational Functions

1.1 Change in Tandem
1.2 Rates of Change
1.3 Rates of Change in Linear and Quadratic Functions
1.4 Polynomial Functions and Rates of Change
1.5 Polynomial Functions and Complex Zeros
1.6 Polynomial Functions and End Behavior
1.7 Rational Functions and End Behavior
1.8 Rational Functions and Zeros
1.9 Rational Functions and Vertical Asymptotes
1.10 Rational Functions and Holes
1.11 Equivalent Representations of Polynomial and Rational Expressions
1.12 Transformations of Functions
1.13 Function Model Selection and Assumption Articulation
1.14 Function Model Construction and Application

**1. Key Concepts in Calculus:**
- Concave Up: Graph curves upward (2nd derivative positive).
- Concave Down: Graph curves downward (2nd derivative negative).
- Inflection Points: Where concavity changes.
- Rate of Change: How fast y changes with x.
- Average Rate of Change: Overall change over an interval.
- Linearity or Quadratic Nature: Identifying linear or quadratic behavior.

**2. Polynomial Functions and Properties:**
- Graphs of Polynomials: Degree, leading coefficient, behavior.
- Local Extrema: Local maxima and minima.
- Absolute Extrema: Highest and lowest points.
- Factoring Polynomials: Breaking them into simpler parts.
- Multiplicity: How many times a root appears.
- Complex Numbers: Real + imaginary parts.
- Even and Odd Functions: Symmetry properties.
- Limit Notation: Behavior near specific values.

**3. Rational Functions and Regression Analysis:**
- Zeros (Roots): Points where the function equals zero.
- Vertical Asymptotes: Lines where function approaches infinity.
- End Behavior: How function behaves at +/- infinity.
- Holes (Point Discontinuities): Removable discontinuities.
- Multiplicity: Number of times a root appears.
- Slant Asymptotes: Diagonal asymptotes.
- Limit Notation: Behavior as x approaches a value.

**4. Binomial Theorem, Function Transformations, and Regression Analysis:**
- Binomial Theorem: Expanding (a + b)^n.
- Function Transformations: Shifting, stretching, reflecting.
- Linear Models: Representing linear relationships.
- Quadratic Models: Describing parabolic shapes.
- Cubic Models: Analyzing cubic relationships.
- Using TI-83 Plus for Regression: Linear, quadratic, and cubic regression with a TI-83 Plus calculator.

These concepts are fundamental in precalculus and serve as building blocks for more advanced mathematical topics.

Nick Perich
Norristown Area High School
Norristown Area School District
Norristown, Pa
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[sallylulu]

it’s 2 am in the morning before my exam and you SAVED me i was so lost before watching through this thank you so much

[davidwaters_]

got my final exam and holy cow the way you explain this is so simple yet so effective thank you so much will be watching al of this and the unit 2 review tonight

[dablaing]

Using these vids to get at least a 4 on my AP test I put my faith in your videos

[sophiaaaaa]

wow, you’re a life saver! i’m currently enrolled in DE (dual enrollment) but taking the ap exam in may and needed some extra review!

[jnoon]

Man I’m am so thankful to find your channel and espiecally this video. I’ve only been in the class for 2 weeks and don’t understand but after watching this I know what I’m doing

[kiwaa]

I wish my teacher actually taught thank you for making these videos i didnt know what a limit was before this 😭

[rishi.bathala]

Thank you so much bro, test on unit 1 next Monday, so I have some prep time. Lifesaver!

[jazlynfisher]

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[billybobbillyboy]

In the 1st 14 minutes i basically understand everything my teachers have given us for our exam reviews, thanks a lot.

[liliannahales]

Unit one final today thank you so so much! My teacher can’t teach like literally can’t answer the questions so you are a life saver. Wish I found you sooner.

[dingle]

Unit 1 test tomorrow… Its good to watch over this and thanks 🤙

[Frank-rs]

For the fraction
It’s 2 times x+1 is 2x+2😅 2:13:21

[emilijuo]

You are goated bro. Test on Wednesday and this vid will be clutch for review this weekend

[lunartoes]

Watching this all for review for my unit test tomorrow, Tysm!!!

[valerimendoza]

Just found your channel and will be making good use of it all. Question. Do you have any Algebra II videos? I see Geometry, Alg 1, Precalc and calc just wondering.

[jlasz]

Hi Mr. goat, me and my buddy been mad struggling to get through this class, as there is very few resources to help students understand. We want to thank for your amazing work. But I have question: what the flip is a residual and why is there no info on ap classroom about them. Our teacher says it’s apart of the unit one curriculum, but very little recourses for calculator inputs and overall equation building could be find. Anyways we love you. Go birds.

[PX-rtjf]

Hello, do you have any videos dedicated to calculator problems for lessons 1.1-1.6.

[SKY-skxl]

sorry for Drake vs. Kendrick situation

[chrisceja]

Hey I have a question, what percent do you think this video covers of all the total units. Its because my teacher had 8 units but everyone says its divided into 4 units

[anthonyzervos]

at 3:03:01 you missed a 1 in front of the 93, silly mistakes right. great video