SOLUTION: Graph the function f(x)= -x, X<3,
3x-4, x>= 3
a) fund the domain
b) locate any intercepts
c) graph the function
d) find the range
e) is f continuous
Algebra.Com
Question 607288: Graph the function f(x)= -x, X<3,
3x-4, x>= 3
a) fund the domain
b) locate any intercepts
c) graph the function
d) find the range
e) is f continuous on its domain?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
a) The function is defined in two different ways for x<3 and for , but it is defined for all x, so the domain is all the real numbers.
b) For x<3, f(x)=-x is a straight line going through the origin, since f(0)=0, so you could say that the x-intercept and the y-intercept are (0,0).
In the other part of the function, for ,
and , so there are no intercepts (no x=0 and no y=0) in that part of the function.
c)
d) f(x)>-3 on both parts of the function, but there is no upper limit. Maybe you would describe the range as (-3,infinity), or maybe you are expected to use a different notation.
e) No. The function is obviously discontinuous at x=3. While it is continuous at all other points of its domain, it is not continuous at all points of the domain.
RELATED QUESTIONS
The function f is defined as follows.
f(x)={x+6 if -5<=x<1}
{9 if x=1}
{-x+4 (answered by jim_thompson5910)
The function f is defined as follows.
f(X)= 6 int(x)
(a) Find the domain of the... (answered by ikleyn)
Given the integer function f(x)= int(2x), find A to D.
A. Find domain.
B. Find... (answered by ikleyn)
For the given rational function f(x) = 3 - 3x over (divided by) x - 5, find the following
(answered by Theo)
Given the piecewise function, find A to D.
f(x) = piecewise function
3x if x does... (answered by ikleyn)
Given the following piecewise function:
{{{f(x)=system(matrix(3,3,
2x-4, for, x<-3,... (answered by Edwin McCravy)
I can not locate given function and locate intercepts of the function can someone help me (answered by nycsub_teacher)
Find the vertex of the graph of the quadratic function. Determine whether the graph... (answered by stanbon)
Locate any intercepts of the function. (Piecewise-defined)
f(x)= {1 if -3 < (answered by stanbon)