1.3 Estimating Limit Values from Graphs

• Steps to estimate the limit of a function from its graph

  1️⃣ Observe the function's behavior as x nears the target value

  2️⃣ Track the y-values of the function as x approaches the target value

  3️⃣ Determine if the y-values approach a specific value
• What is the first step in locating function values on a graph?

  Identify the x-value
• Steps to estimate the limit of a function f(x) as x approaches a target value a.

  1️⃣ Check the left-hand limit

  2️⃣ Check the right-hand limit

  3️⃣ Compare the left-hand and right-hand limits
• Match the technique with its description:

  Observe function behavior ↔️ Look at how the function is behaving near the target value

  Observe function y-values ↔️ Check the y-values as x gets closer to the target value
• The y-value corresponding to a specific x-value on a graph represents the function value at that x.


  True
• Steps to locate function values on a graph

  1️⃣ Identify the x-value

  2️⃣ Locate the x-value on the graph's horizontal axis

  3️⃣ Find the corresponding y-value

  4️⃣ The y-value represents the function value
• The overall limit of a function exists and equals a specific value if both the left-hand limit and right-hand limit exist and are equal
• Steps to determine the overall limit value of a function

  1️⃣ Identify the x-value

  2️⃣ Check the left-hand and right-hand limits

  3️⃣ Ensure both limits exist and are equal

  4️⃣ Conclude the overall limit value
• What is the notation for the limit of a function f(x) as x approaches a?

  $\lim_{x \to a} f(x)$
• What does the limit of a function f(x) as x approaches a represent?

  The value f(x) approaches
• To estimate the limit value from a graph, you need to observe the function values as the input variable approaches the target value.

  True
• If the left-hand and right-hand limits are equal, the overall limit exists.


  True
• If x approaches 3, the target value is 3.

  True
• What does the y-value represent when locating function values on a graph?

  Function value at x
• What are the notations for the left-hand and right-hand limits of a function?

  $\lim_{x \to a^{ - }} f(x)$ and $\lim_{x \to a^{ + }} f(x)$
• Limits are equal when the left-hand and right-hand limits both exist and have the same value.


  True
• Limits describe the value a function approaches as its input approaches a certain point
• The target value of a variable is the value it approaches as it nears a specific point
• To estimate the limit from a graph, observe the y-values as x nears the target value.


  True
• The left-hand limit refers to the value the function approaches as x approaches a target value from the left side.
• The target value of a variable is the value it approaches as it gets closer to a specific point.
• Steps to locate function values on a graph.

  1️⃣ Identify the x-value in the function

  2️⃣ Locate the x-value on the graph's horizontal axis

  3️⃣ Find the corresponding y-value

  4️⃣ The y-value represents the function value at the given x
• When locating function values on a graph, the graph always intersects above the x-value.

  False
• Match the limit type with its definition:

  Left-hand Limit ↔️ Value as x approaches a from left

  Right-hand Limit ↔️ Value as x approaches a from right
• If \lim_{x \to 2^{ - }} f(x) = 4</latex> and $\lim_{x \to 2^{ + }} f(x) =$$4$, then $\lim_{x \to 2} f(x) =$ 4
• Observing the function's behavior as x nears a target value can provide clues about the limit value.


  True
• The target value of a variable is the value it approaches
• The limit value is the value the function approaches as the input variable gets closer to the target value.
• The limit of a function $f(x)$ as $x$ approaches a particular value $a$ is denoted as $\lim_{x \to a} f(x)$ and represents the value the function approaches.
• To locate function values on a graph, first identify the x-value in the function $f(x)$ and locate it on the graph's horizontal axis.
• To locate function values on a graph, the first step is to identify the x value in the function $f(x)$.
• What is the overall limit value of a function denoted as \lim_{x \to a} f(x)</latex>?

  Common value of left and right limits