roster notation - Cabrillo College - Breakthroughs Happen …hpayne/Math...

Math 152 Chapter 2 Handout Helene Payne

Name:

1. The relation {(5, 6), (7, 8), (9, 10)} is given.

(a) Is it a function? Why/Why not?

(b) Find the domain on roster notation.

domain: {

(c) Find the range on roster notation.

range: {

2. The relation {(1, 1), (1, 2), (1, 3)} is given.

(a) Is it a function? Why/Why not?

(b) Find the domain on roster notation.

domain: {

(c) Find the range on roster notation.

range: {


3. Given the functions f(x) = x + 2 and g(x) = x2 − 6, find the indicatedvalues.

(a) f(0)

(b) f(−6)

(c) f(a− 2)

(d) g(−3)

(e) g(2b)

(f) g(f(x))

4. The function R(x) = 1.5x models the total revenue in dollars for a hotdog vendor selling x hot dogs.

(a) Find R(100) with appropriate unit and explain what it is.

(b) Find R(225) with appropriate unit.


5. Graph the functions f(x) = x2 and f(x) = x2− 3 in the same coordinatesystem.

6. Use the vertical line test to find out if the following graphs are the graphof a function. Then find the domain and range on set-builder notation!

(a)

domain range function? yes/no(circle one)


(b)


(c)


7. Which ones of the equations below are linear?

(a) 2x− 5y = 2 Linear / Not Linear (circle one)

(b) 10xz = 5y Linear / Not Linear (circle one)

(c) 2x− 4√

y + 10 = 0 Linear / Not Linear (circle one)

(d) z = 3 Linear / Not Linear (circle one)

(e) x− 2y − 5z + 5w = 1000 Linear / Not Linear (circle one)

(f) y =2

3x2 + 1 Linear / Not Linear (circle one)


8. Find the domain of each function below on set-builder notation!

(a) g(x) = −3x + 2

domain: {

(b) f(x) =1

x + 3

domain: {

9. Given f(x) = 2x− 3 and g(x) = x + 3, find

(a) (f + g)(x)

(b) (f − g)(x)

(c) (f · g)(x)

domain: {(d) (f · g)(−3)

(e) (f

g)(x)

domain: {

(f) (f

g)(−1)


10. A firm making toaster ovens finds that the total cost, C(x), of producingx units is given by C(x) = 40x + 580. The revenue, R(x) from selling xunits is determined by the price per unit ($50) times the number of unitssold, thus R(x) = 50x. Find and interpret (R− C)(92).

11. Use x- and y-intercepts and a check point to graph each equation.

(a) x + y = 5 (b) 3x− 4y = 12


12. Find the slope, m, of the line passing through the points or state that theslope is undefined. Does the line (i) rise, (ii) fall, or is it (iii) horizontalor (iv) vertical?

(a) (2, 1), (3, 6)

slope m =

(i) rise, (ii) fall (iii) horizontal (iv) vertical (circle one)

(b) (1, 4), (1, 8)

slope m =


(c) (−1,−3), (−3, 4)

slope m =


13. Find the slope, m of the given line.

(a) y = 3x− 4

m =

(b) y = −2x

m =


14. Rewrite the given equation in slope-intercept form by solving for y.

(a) 2x− y = 2

slope-intercept form:

(b) x + 3y = 5


15. Graph the equations below:

(a) x = 3 (b) y = −5


16. Find the equation of the line on (i) point-slope form and (ii) on slope-intercept form.

(a) slope = 3, passing through (0, 4)

point-slope form:


(b) slope = −4, passing through (−1,−6)

point-slope form:


(c) passing through (0, 2), (2, 6)

point-slope form:


(d) passing through (−1,−3), (−4,−6)

point-slope form:



17. Find the slope of a line

(a) parallel to the line y = 4x + 1

m =

(b) parallel to the line 3y + 2x = −21

m =

(c) perpendicular to the line y = −3x + 9

m =

(d) perpendicular to the line y + 4x = 1

m =

18. Determine whether the lines y − 2x = 6 and 4y = 2x + 2 are parallel,perpendicular or neither. Show all work and motivate your answer!


19. Find the equation of a vertical line, passing through the point (−20, 8)

20. Find the equation of a horizontal line, passing through the point (−5, 100)

21. Use the given condition to write the equation for a line in slope-interceptform:

(a) passing through (3, 1) and parallel to the line whose equation is2x− y = 7.

(b) passing through (−4, 5) and perpendicular to the line whose equationis y = −3x + 6.

22. An investment is worth $3200 in 2000, by 2005 it has grown to $3700.Let y be the value of the investment in the year x, where x = 0 represents2000.

(a) Determine the slope.

(b) Write a linear equation that models the value of the investment inthe year x.

/ 4 kurgacLtv-ua/u- 7. d tt*u "^t p'1fun. ,7-tt=J&-0)' 'ar1t4 cqrerDdnd-a il not Liruu \5't la'4" g= jx+Ll

+7, t*rr-,ajvolra.'|,';'P'rl'j,9,1;!!l;_r#-ri6) 1s,l,rf d i** . n=Z

") f e ,{ , roJ t) :;;T"^' c) !=:2= z'(x-o)

z o) lo,NLux-uq,hu- 'l'i.',--:H, ^' lrT:-,y^ r,' l corruD"ncl/2fD 9=x'2na-.(,t,A.",orrz-, q;ff.t)G)-=3K

1? a) n=l

,^,v.;rffiQ'uatuu '.lit$tt:;:"+3x_i :l : =;b) 5 tZ a)(t dCs)= o -, al,1

^ = j) i r,'z, zi !(i[di = "", t8 r.: q: 2

3 o) a +) 6)U)

= -: .t-)-' -.= i

Q 'l rc. (R-)04 = s,,l ,"il*, i;iilil,,1c) a- 'in

profr ,:f itting"- rr,,r phpen&a"l"rt) ? f2nillt. n.X:-20^/,, - ^ ilaly_intucert,rr,o)r1 ,r*o 20. y=tao

1l ,!^':,f , ^\ ');:rT;f :;,iif, naz zt o1 s . z,_s

{/ ?(n!"- ?o'!,.ru,-r,,iiy#!,,fiAlm ,l ,, !, "#--.lt+Z)-6=,xt((&))= x'nIx-z [ ,, a]=i ,i'9 22 .^) too ffi'l ,) ,ffi'3,*s.to0:t50

d4b, q U;,Y|.( b) , = oux + 32oo

a) r<czzs) = fi:?Joodyiy ,.') ,#+1i|'* '1 - in ctotta'rr

5 . tl y f, '1{'i'"';*' ts")*3 -,

i - Y'*' afiar 2t

['l f["'4ot"z: '';i ;:':1i4

lxlx i,r rc^fi, r: [:1,',': :{,wj' it-r.^ '7 ,' i , Irl-lr*ssJ t'flo6o) t'

,), ,

c) d:

b)s o)1,t-t--+--)tx

.-r l 'l-q

rcalJ, nol'j\ ., r ',(tf < itr

(ilr}= Kz+lx-2

.-F , 1-+--u

t r '-*18V

6o) t.a)^'.) d'

lxlxi,r *Jl, r:lxl-)-.*3)J,r:

Ix/x;s *4,"ltolrl-3-<xssJ, io

1s rcolJ, nof-jJ, r, frlx

roster notation - Cabrillo College - Breakthroughs Happen …hpayne/Math...

Documents

Transcript of roster notation - Cabrillo College - Breakthroughs Happen …hpayne/Math...