Which of the following is true about the function below? 1/vx-6

Question

2. Which of the following is true about the function below? 1/√x-6
Its domain is (6, ∞) and its range is (-∞, ∞).
Its domain is [6, ∞] and its range is (-∞,0) U (0, ∞) .
Its domain is (6, ∞) and its range is (0, ∞) .
Its domain is (-∞,0) and its range is (0, ∞) .

3. Which of the following statements are true regarding functions? Check all that apply.
A function is a relation in which each value of the input variable is paired with at least one value of the output variable.
A sequence is a function whose domain is the set of natural numbers.
The vertical line test may be used to determine whether a function is one-to-one.
The horizontal line test may be used to determine whether a function is one-to-one.

 

6. It is possible for a system of linear equations to have exactly two solutions.
True
False

7. Let y = 2t + 5 be a linear function representing the distance from home for an ant t minutes after starting out from a location near its home. What does the number 2 represent in this function?
The ant is 2 feet from its home after t minutes.
The ant started out 2 feet from its home.
The ant is crawling at 2 feet per minute.
The ant is moving 2 feet every 5 minutes.

8. Let y = 4t + 2 be a linear function representing the distance from home for an ant t minutes after starting out from a location near its home. What does the number 2 represent in this function?

The ant is 2 feet from its home after t minutes.
The ant started out 2 feet from its home.
The ant is moving at 2 feet per minute.
The ant is moving 4 feet every 2 minutes.

Answer 1

2 None of the choices are correct. the domain's lower bound is 6 but it includes 6, so you need a bracket not a parenthesis. [6, infinity) infinity though is not included, so a bracket for infinity is incorrect. the range is 0 to positive infinity. that assumes you meant 1/sqr(x-6). but if you meant 1/(sqr(x) - 6) still none of the choices are correct

or maybe you meant 1/sqrx - 6? but again, none would be correct

3 a horizontal line test is used to determine if a function is one to one

6 False. A system of 3 linear equations, such as y=0, x=0 and x=1 seemingly have exactly 2 solutions: (0,0) and (0,1). but neither point satisfies all 3 equations. They either all intersect graphically in one point or they don't.

7 the ant is crawling 2 feet per minute

8 the ant started out 2 feet from home. that's what the 2 represents.