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Name:_______________________________________date:______________bk:____

Big Ideas Math 3 Midterm Review

1. Parent functions and transformations

Sketch the parent function. State key information. Ex Key points/domain/range/ intercepts/asymptote /inc/dec…

a. Linear: ( )f x x b. Quadratic 2( )f x x

c. Cubic: 3( )f x x d. Square Roots: ( )f x x

e. Cube Roots: 3( )f x x b. Exponentials ( ) 3xf x

f. Log: 5( ) logf x x

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2. Transformation Time

a. Graph 2

( ) 3 4 2f x x b. Graph (1/2) ( ) 3 2xf x

(1) Describe the transformation

(2)Graph, make sure to label key points

(3) Domain/Range:

c. Graph 6 ( ) 3logf x x d. Graph ( ) 3 4f x x

(1) Describe the transformation

(2)Graph, make sure to label key points

(3) Domain/Range/ Asymptote:

e. Graph 3

( ) 4 3f x x f. Graph ( ) 3f x x

(1) Describe the transformation

(2)Graph, make sure to label key points

(3) Domain/Range

g. Graph 3 ( ) 2 5f x x

(1) Describe the transformation

(2)Graph, make sure to label key points

(3) Domain/Range

(1) Describe the transformations

(2) Graph key points

(3) Domain/Range / Asymptote

(1) Describe the transformations

(2) Graph key points

(3) Domain/Range

(1) Describe the transformations

(2) Graph key points

(3) Domain/Range

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Unit 2: All about quadratics

Unit 2 LT E: I can graph a quadratic function in standard, vertex, or factored form. I can identify the vertex, axis of symmetry,

domain, range and intervals of increase or decrease.

Unit 2 . LT C : I can write a quadratic function in vertex, intercept/factored, or standard form given appropriate information.

4. Write the equation of the parabola with the given characteristics

a. b.

c. Max hits a baseball off a tee that is 3 feet high. The ball reaches a maximum height of 20 feet when it is 15 feet from the tee

d. A grasshopper was standing on the 35 yard line of a football field He jumped, and landed on the 38 yard line At the 36 yard line he was 8 inches in the air.

5. Write an equation of the parabola in intercept/factor form

a.

3.

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6. Unit 2 LT B: I can write and solve systems of equations in 2 or 3 variables

Unit 3A : Everything I ever wonder about polynomials

7. LT A: I can add, subtract, and multiply polynomials. p182 student text

a. b.

c.

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8. LT B: I can divide polynomials synthetically and with long division

LTC: I can expand a polynomial using Pascal’s triangle

9. LT D: I can factor polynomials completely. Techniques to know: GCF factoring, Difference of Squares, Sum or

Difference of Cubes, Binomial factoring, Factoring by Parts as well as multistep factoring that combines these techniques

Factor Completely

a. Factor (basic) b Factor c. Difference of squares

2 5 6x x 22 5 3x x 2 9x 24 81x

d. Difference of cube e. Sum of Cubes f. Quadratic in form

g. Grouping h. Grouping /Difference of squares i. GCF; Quadratic in form

3 23 9 3x x x

j.

4 25 6x x

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Unit 3B : More Fun with polynomials

10.LT B: I can identify the degree and lead coefficient of a polynomial and use it to sketch or write a statement (using

proper notation) about its end behavior.

11. Unit 3B LT C: Given a graph of a polynomial, I can write an equation/function by analyzing roots/x-intercepts and end

behavior

Analyze the graph. (1) Determine the sigh of the leading coefficient. (2) Degree of function. (3) real zeros, (4) write a

polynomial with the least degree & coefficient of 1 in factored form.

a. b.

12. Unit 3B LT D ; I can solve a polynomial by factoring.

a. b.

13. Unit 3B LTF; I can write a polynomial given its roots. I know that irrational and complex roots always occur in conjugate pairs.

Describe the end behaviors

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14. Unit 3B LT H: I can use the Rational Root Thm. to identify possible rational roots, test to find one that “works” and then use the techniques of the chapter to find all roots in the complex number system (Fundamental Thm. of Algebra)

a) ( )

Unit 4: Rational and Radicals

15. LTB : I can simplify radical and rational expressions.

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16. LT C: I can +, -, x functions and evaluate given a specific value.

Given: 2/3( ) 4f x x and 1/3( ) 2g x x , evaluate the following:

a. b. g(x) - f(x)

c. ( )(8)f g d.

Solving with Radicals or Rational Exponents 18. LT D: I can solve radical equations. I know how to check for extraneous solutions.

19. LT F; I can solve radical inequalities and write my answers in interval notation or show them using a numberline.

Inverses

20. LT H; I can find the composition of two functions.& LT I; I can use composition of functions to test or verify if two

functions are inverses.

21. .LT K: I can use algebra to find the inverse of a given function –and determine if the inverse equation is a function

Find the inverse function. Then graph the function and its inverse

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Unit 5 Exponent & Logarithmic Functions Review

Simplifying and Evaluating Logarithms and Exponents

22. LT A: I can use the rules of logarithms to evaluate numerical expressions with exponents or logs.

23. LTB : I can rewrite logarithmic form as exponential and vice versa

Rewrite to logarithmic form

Rewrite to exponential form

24. LT C: I can expand or contract/condense log expressions

Condense the logarithmic expression

25. LT G; I can write an appropriate function given the graph or a written description of the transformations.

Applications

27.LT J: I can use log or exponential solving techniques to find inverse functions algebraically.

3610. log 6

7log 611. 7

ln812. e l313. ln xe

213. 5 3logy x