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# 34

Math 20 Quiz 2

(Write your number in the box above.)

Due: Wednesday, 7-1-2020

Name Denyn Reynolds

(1) Determine whether each of the following defines y as a function of x, (Yes? No?) If NO, briefly

explain why not.

(a) u represents the weight of the 1st class letter, and y is its postage.

(18) yes

(b) 50 students took an exam. x represents student ID, and y represents his/her exam scores.

(1b) yes

For The same test scores x, we may have different (1c)_no

Y

(c) 50 students took an exam. x represents exam scores, and y represents the ID of the student who

got the corresponding scores.

the

no

students ID y

(d) A set of ordered pairs: {(1,1), (-1,1), (2,2), (-2,2), (2,3), (-3,3) }; x is the 1st value,

and is the 2nd value in each pair.

in the set, we have pairs (212) and (2,3), that is for (1d) no

same x value, we have different y value.

(e) A set of ordered pairs: { (3,4), (4,5), (-3, -2), (-2, -1), (2,3), (-3, -4) }; x is

the 1st value, and y is the 2nd value in each pair.

in the set we have pairs (-3,-2) and (-3,-4), that is (16) no

for same x value -3, we have different

Y y

values.

(2) For the following relations, find its domain, range, and determine whether it is a function,

if not, why?

(a) (given by a set of 5 ordered pairs:) {(1,0), (2, -1), (3,0), (4, -1), (5,0) }

Its domain is: { 1,2,3,4,5 }

Its range is: {0,-

}

Is it a function? (if not, why?) yes

ente

qoro

(b) (given by a line segment:)

6

5

Its domain is: [-3,5)

Its range is: [-1,5)

4

3

IN

х

-3-1 0 1 2 3 4 5 6

1

+2

+3

(Use either interval notation or set-builder notation to experss the

domain and range.)

+4

+5

Is it a function? (if not, why?) yes

+6

(c) (given by a table:)

T

-3

– 4

0

-2

– 4

y

5

7

2

5

9

Its domain is: { -3,-4.0)-2,-4 } 1

Its range is: { 5.7,2,5,6

Is it a function? (if not, why?) no

vertical line cuts graph more thom one time. Also, fora

giren value of calmain), we got two different values of (range)

(3) Let f(x) = 5 – 3x and g(x) = 2×2 +1, Find: for example at X=-4, we get y = 7,4

(a) f(-2) = 1 -3X(-2)=57611

(3a) F(-2) – 1

(b) g(-2) = 241-27?H #9

(3b) g(-2):9

(0) (3 – 9) (-4) = 4-3-1-4) – 281-4)2 (8-9)5.382 (30ff-g)(-4)= -16

UT

f -4- 3x f-)

– 4412 – 2x 16

= 4-3X – 2x

16=32

– 116

(d) (fºg)(3) – 4-313)-213)2

(3d) (Fig)(3) –23

– 4-9-18

=-23

(e) f(g(-5)) = 5-3(2x(-5)+1)

(3e) flge-5)) –148

-5-3(51) abr

bugs con

-5-153

(f) f(2a + 1) + g(2a + 1)

(3€) f(2911) Eglan) =80*+za+5

f(294) = 5-362a+ 1) = 5-6a-3 g(2011)-89+278971

f(2a+ 1) = 2-69

38a2+8 at3

= 2.(492+1+49)+1

=> float tgl 29t1) -8a²+2ats

+2975

(4) Graph the following functions in the rectangular system, and write the corresponding letter beside each graph.

=-148

4 2 •

g (2011)= 2 (2971)²+1

2

(c) f(x) = x | -2 > 1X1-2 = (y+2) -\x)

х

(a) f(x) = –2x + 5

)

(b) f(x) = 3

y = 3

↑

不

f(x)

axry=5

ty

6

:

= 1

talle

2.5

5

lit

fa)

$

B

1

0

4

51

19

-6-5-4-3-

х

1

(c)

3

4

-5

-6

(5) Answer the following questions according to the given graph of y = f(x),:

X=-3 y = -2

(a) What is the domain? (5a) [-1,6]

(b) What is the range? (5b) [-2,6]

VI y = 2 f(x)

(c) f(-3) =?

(50)-2

3

(d) f(1) =?

(50) 2

2

–

0

1

2

3

-1

-2

(e) for what values of x does f(x) = 1?

fx

(5e) – 4.50,3.25

X-f1)

(You can estimate the x value by 0.5, 1.5, …)

-3

(f) determine x-intercepts. (5f) – 4,-1,4

(-4,0); H10); (4,0)

fol=1

(g) determine y-intercept. (58)_01

(6) A linear equation 3x – 2y = 6 is given, answer the following questions about this equation:

(a) How many solutions does it have?

(62) Infinitely many

if(y=0) (X,Y)= (20)

dacotta

(b) Fill in the missing x (or y) value so that each pair becomes a solution.

(i) (-2, 6), (ii) (4,3), (iii) (1, -3/2), (iv) (-2,-6),

(c) What is its x-intercept?

(66) 112,0

(d) What is its y-intercept? If(=0) (x,y) = (0,3)

(6)_(0,-3)

(e) Rewrite the equation into its Slope-intercept form

(6)_4 -ŹX-3

3x-2y = 6 – 2y = 3×6 = 3 x – 3

(f) What is the slope of the line of this equation?

(61) _M – Ž

(g) Graph this equation in the following

1 gold

rectangular system.

US!

YA

w

3x-2y=6

6

5

4

7

31

2

1

6-5-4-3-2-11 0

3

4

51

6

X

– 1

4

5

6

Xry +5-2=0

[x+y 13 =0

( m ) = -1

y=x-7

(س)

X

I b (1)

(7) Line li is passing through two points (2, -5) and (-3,0), and Line l2 is the graph of the equaion

x – y = 7. Are they parallel to each other? perpendicular to each other? or neither? Show necessary work.

y-y, = 42-4, (X-XI)

7) perpendicular

X2-X,

х

y (-5)=0+5 (x-2)

X-Y = 1 1 1 mg)=1

-3-2

mixm₂ = -X1

4 15:5 (x-2)

m, x m2 = -1

y t5=-xta

(8) Line li is the graph of 3x + y = 1, and Line l2 is passing through (-6, 1) and perpendicular to li.

Write the equation of l2 in the Slope-intercept form. Show necessary work.

Slope of 1,= -3

(8)_91 = 3x+3.

slope of 12 = -1

. –

–

-3 3

y = mx, to

1-31-6)+

y = 75x, to

-270 Istowwo-8 do

C-3

(-611)

Ji berasal

(9) Write the equation of the line that passes through (-2, 1) and (-3, 4) in its (a) Slope-Intercept

form, and (b) its standard form, show working

TO

y=mxto

(9a) 0 = -2x -5

m=4-1

= 3–3

1919

-3-1-2) –

(95) 3x +y =-5

igorier

1 =-31-2)+c

Mb

y=-387C

1 – O Corcode )

(=-5

gorpo ed in galegos

1-211)

(10) Write the equation of the following line in its (a) Slope-Intercept form, and (b) its standard form,

show work.

3

2

10,-1) (212)

y=mx+6

m-2-1-1) =

2-0

y = 3x +6

10,-1)

-1- 3 xoto

(=.-|

(10a)_Y =ŽX-1

(101)_3x-y=

* (2, 2)

• (0, -1)

Math20 Quiz 2,

40 points.