1) An operator is missing in your statement. Most likely the right expression is:
2x
f(x) = -------------
3x^2 - 3
So, I will work with it and find the result of each one of the statements given to determine their validiy.
2) Statement 1: <span>The
graph approaches 0 as x approaches infinity.
Find the limit of the function as x approaches infinity:
2x
Limit when x →∞ of ------------
3x^2 - 3
Start by dividing numerator and denominator by x^2 =>
2x / x^2 2/x
--------------------------- = ---------------
3x^2 / x^2 - 3 / x^2 3 - 3/x^2
2/∞ 0 0
Replace x with ∞ => ------------ = ------- = ---- = 0
3 - 3/∞ 3 - 0 3
Therefore the statement is TRUE.
3) Statement 2: The graph approaches 0 as x
approaches negative infinity.
</span><span><span>Find the limit of the function as x approaches negative infinity:
2x
Limit when x → - ∞ of ------------
3x^2 - 3
Start by dividing numerator and denominator by x^2 =>
2x / x^2 2/x
--------------------------- = ---------------
3x^2 / x^2 - 3 / x^2 3 - 3/x^2
2/(-∞) 0 0
Replace x with - ∞ => ------------ = ---------- = ---- = 0
3 - 3/(-∞) 3 - 0 3
Therefore, the statement is TRUE.</span>
4) Statement 3: The graph approaches 2/3 as x approaches
infinity.
FALSE, as we already found that the graph approaches 0 when x approaches infinity.
5) Statement 4: The graph approaches –1 as x approaches negative infinity.
</span>
FALSE, as we already found the graph approaches 0 when x approaches negative infinity.
Answer:
Table 1
Step-by-step explanation:
For a function to be linear, equal changes in x must correspond to equal changes in y.
In all tables, the x values increase by 1, so all changes in x in all 4 tables are 1.
If a function is linear, then all changes in y must be equal.
Table 1:
5 - 6 = -1
4 - 5 = -1
3 - 4 = -1
All changes in y are equal, so the first table is linear.
Table 2:
4 - 3 = 1
6 - 4 = 2
Two differences in y are different, so table 2 is not linear.
Table 3:
6 - 7 = -1
5 - 6 = -1
3 - 5 = -2
Not all differences in y are equal, so table 3 is not linear.
Table 4:
4 - 2 = 2
5 - 4 = 1
Not all differences in y are equal, so table 3 is not linear.
The only table that has equal differences in y corresponding to equal differences in x is Table 1, so only Table 1 shows a linear function.
Answer:
24
Step-by-step explanation:
simpley look up the lcm of 6 and 8 and youll get the answer... very simple
