Last Name: First Name:

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2

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(x÷q) 0~J (x-&)

23.) ‘~x+2

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a

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-z—seq.

24.) —~~+i

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Second ExamTrue/False

For #1-8 write the entire word “True” or the entire word “False”.

1.) cz(b+c)=ab+ac

2) ~/~--~VY~V~

3.)~

4.) c’~=v~c’~5.) (~y’=~

6.) (x+y)tz=xht+ytt

7.) (xy)~ =

8.) 7x3 — 12x2 + 3x + 5 has 4 roots.

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Algebra

9.) Find x where 3~4x — 1 = —6.

—~-t~ ~-7

lx:: -

10.) If g(x) is an invertible function, and g(3) = 5, then what is g’(S)?

11.) Find the inverse of f(x) — (3x + 2)~ + 1. (You can check you answerby seeing if f~ o f(x) = x.)

(&~.÷2)3t I

(sx-’z)3

3x÷2

V 1~2

12.) What is the implied domain of g(x) = — 2x + 35x? (Your answershould be an interval.)

3-2~o

3/’‘2:

3x4 — 2x3 — 3x — 3x2—2

3x2-~2x 4~x≤Z_z [ix~~2x3

— (3x~

-C-

— (~zz

4q,f

-12)

—7x÷7

14.) Find3x3 — 2x2 — 3

x—3

3

9 2? ~3

15.) What is the slope of the straight line in R2 that passes throughthe points (2,3) and (6,8)?

13.) Find

S -20-3

3 7 zI:CO

LI.

16.) Complete the square: Write 2x2 + 8x + 4 in the form a(x + /3)2 + ~ywhere cr,/3,-y C R.

17.) How many roots does —3x2 — x + 2 have?

(~Oz~ ~(-3~(2) / + ~(z) ~

18.) Find the roots of 2x2 — 4x + 1

UI) 2(a) 2(z)

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19.) Find a root of x3 + x2 — x + 2

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20.) (2 points) Completely factor 2x3 — 8w2 + 14w — 12. (Hint: 2 is a root.)(Your answer should be a product of a constant and maybe some linear andquadratic polynomials that have leading coefficients equal to 1, and such thatany of the quadratics in the product have no roots.)

2-

-~ 12.

I,

(~)2 ~(z)(~):

≤o 2.1Z4x 6’/e-. (s)(c)<ojlas no

2x3 -

(z-I’/\

2 (xz_az÷3’)

(2 points) Completely factor 3w3 + 5w2 — lix +3.answer should have the same form as described in

J2

3x3÷5t2j~~÷ .3

-3

(3x2~t+x÷)

3 (x-i) (x-’4’)-z ‘4

2. -8Lj.

Jt~- -12

2.. -If‘0

21.)(Your

-3 3 5 -H 3

(Hint:#20.)

-3 is a root.)

54 3xz~Y-x+I has two r~ow

If

1÷2

-r

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Graphs

22.) List all of the monic linear factors of p(x) that you know of from thegraph below.

23.) Graph ?/x +2 and label its x-intercept.

sk;c~ ~Ct 2.

24.) Graph —~/~ + 1 and label its y-intercept.

-4;); ogtC )L41X1 s111C~ i.iI.25.) Graph —3x + 2 and label its x- and y-intercepts.

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26.) Graph 3(x + 1)2 + 2 and label its vertex.

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2.