Question

Which of the following are characteristics of the graph of the reciprocal parent function? check all that apply

Answer 1

3 answers: Choice A, Choice C, Choice D

Basically, everything but choice B

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Explanation:

Lets go through the answer choices to see which are true or false.

For each, we'll be considering the graph of y = 1/x as shown below.

• A. True. We have two branches that are completely separate and never meet up, and those two branches are in quadrants Q1 and Q3. Both curves are always decreasing (going downhill as you move from left to right). This is because if x is positive, then so is y = 1/x. If x is negative, then so is y = 1/x. Any point (x,y) is either composed of two positive coordinates or two negative coordinates.
• B. False. A parabola is one single curve and we have two separate curves here.
• C. True. A hyperbola is composed of two curves as the graph of y = 1/x shows.
• D. True. The graph shows y = 1/x does not go through the origin. This is because we cannot have x = 0 in y = 1/x, or otherwise we have a division by zero error. A similar situation happens with y = 0 as well.