Question
Asked Sep 10, 2019
GRAPHS AND FUNCTIONS
Graphing a piecewise-defined function: Problem type
Suppose that the function g is defined, for all real numbers, as follow
if x3
2
g (x)
if x=3
5
Graph the function g.
help_outline

Image Transcriptionclose

GRAPHS AND FUNCTIONS Graphing a piecewise-defined function: Problem type Suppose that the function g is defined, for all real numbers, as follow if x3 2 g (x) if x=3 5 Graph the function g.

fullscreen
check_circleExpert Solution
Step 1

The function has a break at x = 3. We need to evaluate if the function is continuous at x = 3.

Step 2

As we approach x = 3 from the left hand side we get, g(3 - h) = - (3 - h) / 2 = - 3 / 2

As we approach x = 3 from the right hand side we get, g(3 + h) = - (3+ h) / 2 = - 3 / 2

g(3) = 5

Since the left hand limit = right hand limit, but they ae not equal to the value of the function at the given point, hence the given function is not continuous at x = 3.

 

Step 3

The table for plot will be as show on...

g(x)
X
2.50
-5.00
-4.00
2.00
-3.00
1.50
-2.00
1.00
-1.00
0.50
O.00
0.00
1.00
-0.50
2.00
-1.00
3.00
5.00
4.00
-2.00
5.00
-2.50
help_outline

Image Transcriptionclose

g(x) X 2.50 -5.00 -4.00 2.00 -3.00 1.50 -2.00 1.00 -1.00 0.50 O.00 0.00 1.00 -0.50 2.00 -1.00 3.00 5.00 4.00 -2.00 5.00 -2.50

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour*

See Solution
*Response times may vary by subject and question
Tagged in

Math

Calculus

Functions