Honors Pre-Calc Unit 1 Review Jeopardy

Piecewise Functions

100

What are the equations in this function?

Write it as f(x)={ AND include any Domain restrictions

https://ds055uzetaobb.cloudfront.net/brioche/uploads/rHtkgZFatd-group-57.svg?width=300

 f(x)={

y=⁵⁄₃x+¹¹⁄₃ -4≤x≤-1

y=2 -1≤x≤3

y=-2 3≤x≤4

         

200

What are the equations in this function?

Write it as f(x)={ AND include any Domain restrictions

https://mathbitsnotebook.com/Algebra1/FunctionGraphs/PWprac2.jpg

f(x)={

2 x<-1

(x+1)² -2 x≥-1

300

Draw the complete function:

f(x)={

¼x-0.5 x≤-2

2-√2x 0≤x<2

https://d138zd1ktt9iqe.cloudfront.net/media/seo_landing_files/piecewise-function-graph-1640667678.png 

400

DOUBLE POINTS

Draw the complete function:

f(x)={

x² x≤0

x 0<x≤2

3 x>2

DOUBLE POINTS

https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/1227/2015/04/03010549/CNX_Precalc_Figure_01_02_0262.jpg

500

What are the equations in this function?

Write it as f(x)={ AND include any Domain restrictions

https://www.efofex.com/documentation/fxgclip0351.png 

f(x)={ 

-1+2 x<-1

½x²  -1≤x≤2

-√x-2+2 x>2

Domain Restrictions

100

Write the Domain for the function

https://mathbitsnotebook.com/Algebra2/Quadratics/parabolaplot1.jpg

All real #s

200

Write the Domain for the function

https://www.mathguide.com/lessons2/Functions/pb3.gif

x<0

x≤0

300

Write the Domain for the function

https://o.quizlet.com/w2sow4eLlwGJK.15.eO1Mw.png

x<-2

x≥-2

400

Write the Domain for the function

https://www.ixl.com/~media/1/Ama2PuSYQYETswGiWVW_-7xtVTvcz2unbQJeP9sgWypz5H75YDjeul1Qkgt8RR3DwJ4yVuItSDXcIxhf6eiLQe2CmVgr9aC3vl2-SjNPA2w.svg

x<-2

-2≤x<3

x≥3

500

Write the Domain for the function

https://homework.study.com/cimages/multimages/16/geo_0830443938691652166429.png

x≤-1

-1<x<4

4≤x

Composing Functions

100

Let f(x)=2x+3 and g(x)=x²

find f(g(x))

f(g(x))=2x²+3

200

Let f(x)=¹⁄ₓ and g(x)=√ 3-x

find f(g(x))

f(g(x))=¹⁄√₃₋ₓ

300

Let f(x)=3x-4 and g(x)=¹⁄ₓ₋₂

find f(g(x))

f(g(2))=-¹³⁄₄

400

Find f(g(1))

https://cdnapisec.kaltura.com/p/2172211/thumbnail/entry_id/1_gwyka25c/def_height/500/def_width/500/

f(g(1))=2

500

DOUBLE POINTS

Let f(x)= ⁴⁄ₓ₋₃ and g(x)=2x-5

find f(g(x))

DOUBLE POINTS

f(g(x))=⁻⁴⁄₂ₓ₋₅ -3

Finding Inverses

100

What makes 2 functions Inverses of each other?

If both functions are equal to x

200

Verify if the following functions are inverses:

f(x)=∛x - 1 g(x)=(x + 1)³

f(x)=x g(x)=x

Inverses

300

Find the inverse of f(x)

f(x)=³ˣ⁻⁵⁄₂

f^-1(x)=²ˣ⁺⁵⁄₃

400

Verify if the following functions are inverses:

f(x)= -7(x+2) + 6 and g(x)= ∛-⁽ˣ⁻⁶⁾⁄₇ -2

f(g)= x g(f)=x

Inverses

500

Verify if the following functions are inverses:

f(x)=∛2x + 5 -3 

g(x)= (x+3)³ - 5/2 + 1

g(x)= x+1 NOT INVERSES

Factoring Binomials/Trinomials

100

Multiply (x - 4)(x + 4)

x² - 16

200

(x - 2)(x² + 2x + 4)

(x³ - 8)

300

Factor the difference of squares: 49x² - 81

49x² - 81 = (7x + 9)(7x - 9)

400

DOUBLE POINTS

Factor  216x³ + 27

DOUBLE POINTS

(6x + 3)(36x² - 18x + 9)

500

Factor: 6,859x³ + 343

(19x + 7)(361x² -133x + 49)