Piecewise function - help needed

[terriroze]

Given the following piecewise function:
f(x) = {(x + 4 for x < -3)(-1 for -3 <= x < 5)(2x for x > 5)}

a. find the domain
b. find the range
c. find the intercepts
d. is f continous on its domain? If not, stae where f is discontinous.
e. graph the function

Please show all the steps.

Thank you.

 

[Deleted member 4993]

Given the following piecewise function:
f(x) = {(x + 4 for x < -3)(-1 for -3 <= x < 5)(2x for x > 5)}

a. find the domain
b. find the range
c. find the intercepts
d. is f continous on its domain? If not, stae where f is discontinous.
e. graph the function

Please show all the steps.

Thank you.

What are the definitions of domain, range and intercepts?

Please share your work with us, indicating exactly where you are stuck - so that we may know where to begin to help you.

 

[terriroze]

Piecewise function - work attached now. Thank you. Please HELP!

What are the definitions of domain, range and intercepts?

Please share your work with us, indicating exactly where you are stuck - so that we may know where to begin to help you.

This is what I have. I don't even know if any of this is correct.


I am sooooo confused.

I am just guessing.

1. Given the following piecewise function:

x+4 for x < -3
f(x) = -1 for -3 < x < 5
2x for x > 5

1. Find the domain.
2. Find the range.
3. Find the intercepts.
4. Is f continuous on its domain? If not, state where f is discontinuous.
5. Graph the function.

f(x) = x = x if x > 0
-x if x <0

Find f(0)
x=0
f(x) = x+4
f(0) = 0+4 = 4

When x = 1, the equation for f is f(x) = -1
f(1) = -1

When x = 2, the equation for f is f(x) = 2x
f(2) = 2(2) = 4

1. Find the domain. The domain of f is {x|x > 5}, or the interval (5,oo)

1. Find the range: (-oo, 1) U (10, + oo)

Graph to find range
y = x + 4
0 = x + 4
-4 = x
x-intercept: (-4, 0)

y= x -1
y = 0 – 1
y = -1
y-intercept: (0, -1)


y = 2x
y = 2(3)
y = 6
intercept (3, 6)

y = 2x
y = 2(4)
y = 8
Intercept (4, 8)

y = 2x
y = 2 (5)
y = 10
intercept (5, 10)

y = x + 4
y = 5 + 4
y = 9
intercept (5, 9)

y = x + 4
y = 6 + 4
y = 10
intercept (6, 10)

1. Find the intercepts

y = x+4
0 = x + 4
-4 = x
x-intercept: (-4, 0)


y= x -1
y = 0 – 1
y = -1
y-intercept: (0, -1)

1. Is f continuous on its domain? If not, state where f is discontinuous.

No. Discontinuous at x = -3 and at x =5

Look at the middle equation to answer this. -3 < x < 5