Use the graphs of the rational functions in choices A–D to answer each question. There may be more than one correct choice. Which choices have domain (-∞, 3)U(3, ∞)?

Question

Use the graphs of the rational functions in choices A–D to answer each question. There may be more than one correct choice.  Which choices have domain (-∞, 3)U(3, ∞)?

Accepted Answer

Welcome back. I am so glad you're here. We are asked to identify the graph of the rational function having a domain of open parentheses, negative infinity comma five close parentheses in union with open parentheses, five comma infinity closed parentheses. And for our answer choices, we have four graphs, we will look at all of those graphs in detail comparing them in a moment. First, let's talk about what it means to have a graph for a rational function with the domain of negative infinity to five in union with five to infinity. The key part here is these parentheses, the parentheses are around five which tells us that five is not included in our domain. Now, what does that mean in terms of a graph? Well, that means that we're looking for a graph where positive five is not included and it would show that five is not included. The X value of five is not included by giving us a vertical asom tote. And recalling from previous lessons, vertical asom totes are shown with an up and down dotted line, that's a vertical ASOM tote. And that will be right at the X value of positive five and then the function lines will be drawn around it close to it but not touching it. So now let's compare our graphs. Well, answer choice A, they have a vertical asom tote that dashed line right at X equals five. So that's promising. Let's check out the other ones to make sure we're not missing anything. Answer choice B has a vertical asom tote that dashed line at an X value of negative five. That's not gonna work. This would have the domain written as open parentheses, negative infinity comma negative five closed parentheses in union with open parentheses, negative five comma per infinity closed parentheses. Answer to ac well, they have an ASOM tote at an X value of negative four. So that's not what we're looking for. We want it. And you can see that the line goes right over the X value of positive five. So answer choice C doesn't work. An answer. Choice D is awfully close, but that's a positive four, not a positive five. So this graph does go through positive five. Then the vertical asom tote is that X equals four for answer choice D. So we were correct when we identified answer choice. A well done, we'll catch you on the next one.

Use the graphs of the rational functions in choices A–D to answer each question. There may be more than one correct choice. Which choices have domain (-∞, 3)U(3, ∞)?

Verified Solution

Key Concepts

Rational Functions

Domain of a Function

Interval Notation