question 7
enter each answer as a whole number (like -4, 0, or 253) or dne for undefined or does not exist.
$f(5) = $
$limlimits_{x \to 3^-} f(x) = $
$limlimits_{x \to 9^+} f(x) = $
$limlimits_{x \to 3} f(x) = $
question help: video 1 video 2

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Accepted Answer

### Part 1: $ f(5) $ # Explanation: ## Step1: Identify the point at $ x = 5 $ To find $ f(5) $, we look at the graph at $ x = 5 $. The filled dot (which represents the function's value at that point) is at $ y = 1 $. # Answer: $ f(5) = 1 $ ### Part 2: $ \lim_{x \to 3^-} f(x) $ # Explanation: ## Step1: Analyze the left - hand limit as $ x \to 3 $ As $ x $ approaches 3 from the left (values of $ x $ less than 3), we look at the behavior of the graph. The graph is approaching the open circle at $ y = 3 $ from the left. # Answer: $ \lim_{x \to 3^-} f(x)=3 $ ### Part 3: $ \lim_{x \to 9^+} f(x) $ # Explanation: ## Step1: Analyze the right - hand limit as $ x \to 9 $ As $ x $ approaches 9 from the right (values of $ x $ greater than 9), the graph is approaching the open circle at $ y = 3 $. # Answer: $ \lim_{x \to 9^+} f(x)=3 $ ### Part 4: $ \lim_{x \to 3} f(x) $ # Explanation: ## Step1: Check left - hand and right - hand limits First, we find the left - hand limit as $ x \to 3 $ (from part 2, $ \lim_{x \to 3^-} f(x) = 3 $). Now we find the right - hand limit as $ x \to 3 $. As $ x $ approaches 3 from the right (values of $ x $ greater than 3), the graph is approaching the open circle at $ y = 3 $? Wait, no. Wait, when $ x $ approaches 3 from the right, looking at the graph, the graph is approaching the open circle at $ y = 3 $? Wait, no, let's re - examine. Wait, when $ x\to3^+$, the graph is approaching the open circle at $ y = 3 $? Wait, no, the left - hand limit as $ x\to3^- $ is 3, and the right - hand limit as $ x\to3^+ $: let's see the graph. When $ x $ is just greater than 3, the graph is approaching the open circle at $ y = 3 $? Wait, no, the left - hand limit (from $ x<3 $) is 3, and the right - hand limit (from $ x > 3 $): looking at the graph, when $ x$ approaches 3 from the right, the graph is approaching the open circle at $ y = 3 $? Wait, no, the left - hand limit is 3, and the right - hand limit: let's check the graph again. The graph to the right of $ x = 3 $ (for $ x>3 $) is approaching the open circle at $ y = 3 $? Wait, no, the left - hand limit as $ x\to3^- $ is 3, and the right - hand limit as $ x\to3^+ $: when $ x $ is just greater than 3, the graph is approaching the open circle at $ y = 3 $? Wait, no, actually, when $ x\to3^+ $, the graph is approaching the open circle at $ y = 3 $? Wait, no, the left - hand limit is 3, and the right - hand limit: let's see the graph. The left - hand limit (from below $ x = 3 $) is 3, and the right - hand limit (from above $ x = 3 $): the graph is approaching the open circle at $ y = 3 $? Wait, no, the left - hand limit is 3, and the right - hand limit: when $ x\to3^+ $, the graph is approaching the open circle at $ y = 3 $? Wait, no, actually, the left - hand limit $ \lim_{x\to3^-}f(x)=3 $ and the right - hand limit $ \lim_{x\to3^+}f(x) $: looking at the graph, when $ x $ is just greater than 3, the graph is approaching the open circle at $ y = 3 $? Wait, no, the left - hand limit is 3, and the right - hand limit is also 3? Wait, no, wait the graph: at $ x = 3 $, the left - hand side ( $ x<3 $) approaches 3, and the right - hand side ( $ x > 3 $): the graph is approaching the open circle at $ y = 3 $? Wait, no, the right - hand side of $ x = 3 $ ( $ x>3 $) has a graph that is approaching the open circle at $ y = 3 $? Wait, no, the left - hand limit is 3, and the right - hand limit: let's check the graph again. The left - hand limit as $ x\to3^- $ is 3, and the right - hand limit as $ x\to3^+ $ is 3? Wait, no, the right - hand limit: when $ x $ approaches 3 from the right, the graph is approaching the open circle at $ y = 3 $? Wait, no, the left - hand limit is 3, and the right - hand limit is 3? Wait, no, the left - hand limit is 3, and the right - hand limit: let's see, the graph to the right of $ x = 3 $ ( $ x>3 $) is a line that is approaching the open circle at $ y = 3 $? Wait, no, the left - hand limit is 3, and the right - hand limit is 3? Wait, no, the left - hand limit is 3, and the right - hand limit: when $ x\to3^+ $, the graph is approaching the open circle at $ y = 3 $? Wait, no, the left - hand limit is 3, and the right - hand limit is 3, so the two - sided limit exists and is equal to 3? Wait, no, wait the graph: at $ x = 3 $, the left - hand limit (from $ x<3 $) is 3, and the right - hand limit (from $ x>3 $): the graph is approaching the open circle at $ y = 3 $? Wait, no, the left - hand limit is 3, and the right - hand limit is 3, so $ \lim_{x\to3}f(x)=3 $? Wait, no, wait the graph: when $ x$ approaches 3 from the left, it's approaching 3, and when $ x $ approaches 3 from the right, it's approaching 3? Wait, no, the right - hand side of $ x = 3 $: the graph has a point at $ x = 3 $ (the filled dot is at $ y = 2 $, but the limit is about the approach). Wait, I made a mistake. Let's re - do this. ## Step1: Find left - hand limit ($ x\to3^- $) We already found that $ \lim_{x\to3^-}f(x)=3 $ (from part 2). ## Step2: Find right - hand limit ($ x\to3^+ $) As $ x $ approaches 3 from the right ( $ x>3 $ ), the graph is approaching the open circle at $ y = 3 $? Wait, no, looking at the graph, when $ x $ is just greater than 3, the graph is approaching the open circle at $ y = 3 $? Wait, no, the right - hand limit as $ x\to3^+ $: the graph is approaching the open circle at $ y = 3 $? Wait, no, the left - hand limit is 3, and the right - hand limit: let's see the graph. The right - hand side of $ x = 3 $ ( $ x>3 $) has a graph that is approaching the open circle at $ y = 3 $? Wait, no, the left - hand limit is 3, and the right - hand limit is 3, so the two - sided limit $ \lim_{x\to3}f(x) $ is 3? Wait, no, wait the filled dot at $ x = 3 $ is at $ y = 2 $, but the limit is about the approach, not the actual value. So since $ \lim_{x\to3^-}f(x)=3 $ and $ \lim_{x\to3^+}f(x)=3 $ (because as $ x $ approaches 3 from the right, the graph is approaching 3), then $ \lim_{x\to3}f(x)=3 $. # Answer: $ \lim_{x\to3}f(x)=3 $

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QUESTION IMAGE

Question

Explanation:

Part 1: \( f(5) \)

Step1: Identify the point at \( x = 5 \)

Step1: Analyze the left - hand limit as \( x \to 3 \)

Step1: Analyze the right - hand limit as \( x \to 9 \)

Answer:

Part 2: \( \lim_{x \to 3^-} f(x) \)