## Discontinuity Graphs Homework Help!!!!

Limits, differentiation, related rates, integration, trig integrals, etc.
kathrynm77
Posts: 3
Joined: Wed Sep 26, 2012 11:40 pm
Contact:

### Discontinuity Graphs Homework Help!!!!

I think most of my answers are right but need confirmation

The directions are to ....

a) Make a sketch of the graph
b) Represent any points of discontinuity with a hole
c) Name domain and range
d) Where appropriate, simplify and name new function

__________________________________________________ ____________
1. h(x) = sqrt(3x-4)
a) upper half of sideways parabola infirst quad starting at x=4/3
but i dont know what the y-value is
b) no holes?
c) D=[4/3,inf)
R= ?
d) cant be simplified
__________________________________________________ ___________
2. F(x)= (4x2-1)/(2x+1)
a)line with positive slope with y int at -1
b) hole at (-1/2,-2)
c) D=(-inf,-1/2),(-1/2,inf)
R=(-inf, -2), (-2,inf)
d) new function = 2x-1
__________________________________________________ _____________-
3. f(x)=(x2-4x+3)/(x-1)
a) line with positive slope with y-int at -3
b) hole at (1,-2)
c) D=(-inf, 1),(1,inf)
R=(-inf,-2),(-2,inf)
d) new function = x-3
__________________________________________________ ______________
4. This ones a piecewise function
f(x)={2x-1 if x cant equal 2
{0 if x=2
a)line with y int at -1 and point at (2,0)
b) hole at (2,3)
c) D=all reals
R=(-inf,3), (3,inf)
d)cant be simplified
__________________________________________________ _____________
5. also a piecewise function
h(x)={x+6 if x is less than or equal to -4
{sqrt(16-x2) if -4<x<4
{6-x if x is greater than or equal to 4
a) semi circle in top half of graph with ends at 4 and -4 but open circles, one line with negative slope in second quad above x-axis at -4 and the same image flipped in other quad
b) holes at (-4,0) and (4,0)
c) D= all reals
R=(-inf, 4)
d) cant be simplified
__________________________________________________ ______________
6. also piecewise function
g(x)={x-2 if x<0
{0 if x=0
{x2+1 if x>0
a)right side of parabola with open circle on y int, point at the origin, line with negative slope y-int at -2 as open circle
b)holes at (0,1) and (-2,0)
c) D=all reals
R=(-inf,-2),[2,2],(1,inf)
d) cant be simplified
__________________________________________________ ______________
7. F(x)= (x3+3x2+x+3)/(x+3)
a) parabola centered at origgin with hole at x-value of -3
b) hole at (-3,10)
c) D=(-inf, inf),(x cant equal -3)
R= [0,inf), (y cant equal...10?)
d) new function = x2+1
__________________________________________________ _______________
Thanks

Posts: 136
Joined: Sun Feb 22, 2009 11:12 pm

### Re: Discontinuity Graphs Homework Help!!!!

1. h(x) = sqrt(3x-4)
a) upper half of sideways parabola infirst quad starting at x=4/3
but i dont know what the y-value is
b) no holes?
c) D=[4/3,inf)
R= ?
d) cant be simplified
a) yes (and plug the x in to find the y), b) look at the graph!, c) yes and look at the graph, d) yes
2. F(x)= (4x2-1)/(2x+1)
a)line with positive slope with y int at -1
b) hole at (-1/2,-2)
c) D=(-inf,-1/2),(-1/2,inf)
R=(-inf, -2), (-2,inf)
d) new function = 2x-1
a) yes, b) yes, c) yes, d) yes (but restrict the domain to "x not equal to -1/2")
3. f(x)=(x2-4x+3)/(x-1)
a) line with positive slope with y-int at -3
b) hole at (1,-2)
c) D=(-inf, 1),(1,inf)
R=(-inf,-2),(-2,inf)
d) new function = x-3
a) yes, b) yes, c) yes, d) yes (but restrict)
4. This ones a piecewise function
f(x)={2x-1 if x cant equal 2
{0 if x=2
a)line with y int at -1 and point at (2,0)
b) hole at (2,3)
c) D=all reals
R=(-inf,3), (3,inf)
d)cant be simplified
a) yes, b) no (look at the graph!), c) no, d) no
5. also a piecewise function
h(x)={x+6 if x is less than or equal to -4
{sqrt(16-x2) if -4<x<4
{6-x if x is greater than or equal to 4
a) semi circle in top half of graph with ends at 4 and -4 but open circles, one line with negative slope in second quad above x-axis at -4 and the same image flipped in other quad
b) holes at (-4,0) and (4,0)
c) D= all reals
R=(-inf, 4)
d) cant be simplified
a) i think so (words are hard to "see"), b) yes, c) yes, d) yes
6. also piecewise function
g(x)={x-2 if x<0
{0 if x=0
{x2+1 if x>0
a)right side of parabola with open circle on y int, point at the origin, line with negative slope y-int at -2 as open circle
b)holes at (0,1) and (-2,0)
c) D=all reals
R=(-inf,-2),[2,2],(1,inf)
d) cant be simplified
a) i think so, b) no (i think one of your points is backwards), c) no (look at the graph), d) yes
7. F(x)= (x3+3x2+x+3)/(x+3)
a) parabola centered at origgin with hole at x-value of -3
b) hole at (-3,10)
c) D=(-inf, inf),(x cant equal -3)
R= [0,inf), (y cant equal...10?)
d) new function = x2+1
a) i think so (not sure about "centered at origin"), b) yes, c) yes, d) yes (but restrict)

hope that he,lps

kathrynm77
Posts: 3
Joined: Wed Sep 26, 2012 11:40 pm
Contact:

### Re: Discontinuity Graphs Homework Help!!!!

yes thankyou so so much...however could you explain why number 4 and 6 are wrong..thanks!