i wasn't sure on how to explain it so i just attached ur answer
A pack of 5 of board games costs $75.
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Answer:
D. I, II, and III
Step-by-step explanation:
A discontinuous function is a function which is <u>not continuous</u>.
If f(x) is not continuous at x = a, then f(x) is said to be discontinuous at this point.
To prove whether a function is <u>discontinuous</u>, find where it is undefined.
A rational function is <u>undefined</u> when the <u>denominator</u> is equal to zero.
Therefore, to find the values that make a rational function undefined, set the <u>denominator to zero</u> and <u>solve</u>.
<u>Function I</u>
Denominator: x - 2
Set to zero: x - 2 = 0
Solve: x = 2
Therefore, this function is undefined when x = 2 and so the function is discontinuous.
<u>Function II</u>
Denominator: 4x²
Set to zero: 4x² = 0
Solve: x = 0
Therefore, this function is undefined when x = 0 and so the function is discontinuous.
<u>Function III</u>
Denominator: x² + 3x + 2
Set to zero: x² + 3x + 2 = 0
Solve:
⇒ x² + 3x + 2 = 0
⇒ x² + x + 2x + 2 = 0
⇒ x(x + 1) + 2(x + 1) = 0
⇒ (x + 2)(x + 1) = 0
⇒ x = -2, x = -1
Therefore, this function is undefined when x = -2 and x = -1, and so the function is discontinuous.
Therefore, <u>all</u> three given functions are discontinuous.
