Graph the function.
g(x)={x+2, x less than or equal to -3
1/2x-2, x>-3
for x < -3 , sketch the line y = x+2
put an "open" point at (-3,-1) , showing the point is excluded
for x≥-3, sketch y = (1/2)x - 2
draw a "closed' point at (-3, -5/2) , showing that point is included.
It's still giving me the wrong answer. and how do I plot -5/2, when the graph shows no decimals?
If you are doing this kind of math, I am surprised that you didn't know that
-5/2 = -2.5 or -2 1/2
What do you mean by "it's still giving me the wrong answer" , what is "it"
The table plot on my homework is givving me the wrong answer.
I did not read your question carefully enough
change it to:
for x ≤ -3 , sketch the line y = x+2
put an "closed" point at (-3,-1) , showing the point is included
for x>-3, sketch y = (1/2)x - 2
draw a "open' point at (-3, -7/2) , showing that point is excluded.
notice the second point is (-3, -7/2) or (-3, =3.5)
try it now.
The only other thing that could be wrong is that your second equation is
y = 1/(2x) -2 , but I doubt it.
To graph the function g(x), we need to plot the points on a coordinate plane based on the given conditions.
For x less than or equal to -3 (x ≤ -3):
In this case, the function is g(x) = x + 2. We start by selecting some x-values that are less than or equal to -3, then calculate the corresponding y-values by substituting these x-values into the equation.
Let's choose x = -4 as our first x-value:
g(-4) = -4 + 2 = -2
So, we have the point (-4, -2).
Next, let's choose x = -5:
g(-5) = -5 + 2 = -3
So, we have the point (-5, -3).
Now, let's plot these two points on the graph.
For x > -3 (x > -3):
In this case, the function is g(x) = (1/2)x - 2. Again, we select some x-values that are greater than -3 and find the corresponding y-values.
Let's choose x = 0 as our first x-value:
g(0) = (1/2)(0) - 2 = -2
So, we have the point (0, -2).
Next, let's choose x = 2:
g(2) = (1/2)(2) - 2 = -1
So, we have the point (2, -1).
Now, let's plot these two points on the graph as well.
After plotting all the points, we can join them with a dotted line (since the function is defined separately for different ranges of x) to get the graph of the function g(x).
In summary, the graph will include the points (-4, -2), (-5, -3), (0, -2), and (2, -1), connected with a dotted line.