Graph g(x)= 2x+8 if x<-2
. 5-2x if -2 is less than or greater than x < 3
-2 if x is greater than or less than 3
I have to graph this and I have no idea?! Please help!!
Of course you have some idea. Surely you can graph
y = 2x+8
Draw that line, but stop at x=-2
Then between x = -2 and x=3, draw the graph of
y = 5-2x
Then for x beyond 3, draw the graph of
y = -2.
Just take it slowly and do one step at a time.
Thanks Steve!
To graph the function g(x) with multiple pieces, we will follow these steps:
Step 1: Find the domain of the function
The domain of the function is the set of all possible x-values for which the function is defined. In this case, we have three different pieces, each defined for different intervals of x. The domain consists of the union of the individual domains for each piece.
Domain:
For the first piece, x <- 2, there are no restrictions.
For the second piece, -2 < x < 3, x is defined within this interval.
For the third piece, x > 3, there are no restrictions.
So, the domain of the function g(x) is all real numbers.
Step 2: Evaluate the function for important x-values
To plot the graph, we need to determine the y-values for certain key x-values within each interval defined by the pieces of the function.
Piece 1 (x < -2):
Choose an arbitrary value for x that is less than -2, let's say x = -3.
g(x) = 2x + 8
g(-3) = 2(-3) + 8
g(-3) = 2(-3) + 8
g(-3) = -6 + 8
g(-3) = 2
So, when x < -2, g(x) = 2.
Piece 2 (-2 < x < 3):
Choose an arbitrary value for x within this interval, let's say x = 0.
g(x) = 5 - 2x
g(0) = 5 - 2(0)
g(0) = 5 - 0
g(0) = 5
So, when -2 < x < 3, g(x) = 5 - 2x.
Piece 3 (x > 3):
Choose an arbitrary value for x that is greater than 3, let's say x = 4.
g(x) = -2
g(4) = -2
So, when x > 3, g(x) = -2.
Step 3: Plot the points on a graph
Now we have the following points:
(x, g(x)):
(-∞, 2) for x < -2
(-2, 5) for -2 < x < 3
(3, -2) for x > 3
We can now plot these points on a graph and connect them.
Lastly, label the graph and include the domain as discussed earlier.
I hope this explanation helps you graph the function g(x) effectively!