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:
x = -2 ±√5
Step-by-step explanation:
You want to complete the square by adding the square of half the coefficient of the linear term:
x^2 + 4x + (4/2)^2 = 1 + (4/2)^2
(x +2)^2 = 5 . . . . . simplify
x +2 = ±√5 . . . . . . take the square root
x = -2 ±√5 . . . . . . subtract 2. This is the solution.
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For the problem in the picture, replace x with p in the above.
Tax credits provide dollar for dollar reduction of the persons income. meaning $1,000 tax credit saves $1,000 taxes.
Tax deductions lower taxable income and then they equal the % of the persons marginal tax bracket
