Which graph represents the function? g(x)={x if x<2−3 if x≥2
2 answers:
Answer:
We have to graph the function g(x) which is given as:
g(x)= x when x<2
and -3 when x ≥2.
Clearly after looking at the function we see that the function is not continuous since we find the continuity at x=2 as follows.
Left hand limitat 2:
g(2-h)=lim h→0 2-h
=2-0=2
Also right hand limit at x=2 is:
g(2+h)=lim h→0 (2+h)
= 2+0=2
Also g(2)= -3.
As:
Left hand limit= Right hand limit but is not equal to function's value at that point.
Hence, the function is discontinuous at x=2.
so for x<2 we will get a graph of a line y=x.
and for x≥2 we will get a straight line y=-3 parallel to the domain.
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Answer: C. The equations have the same solution because the second equation can be obtained by adding 6 to both sides of the first equation.
Step-by-step explanation:
You know that the first equation is:
And the second equation is:
According to the Addition property of equality:
If ; then
Then, you can add 6 to both sides of the first equation to keep it balanced. Then, you get:
Therefore, you can observe that the second equation can be obtained by adding 6 to both sides of the first equation, therefore, the equations have the same solution.
If you want to verify this, you can solve for "x" from both equations:
- First equation:
- Second equation: