Use the graphs to answer each item. Do not use a calculator....

Use the graphs to answer each item. Do not use a calculator. The graph of $y=f(x)$ gives the speed limit $y$ along a rural highway after traveling $x$ miles. (GRAPH NOT COPY) A. What is the speed limit at the 4 -mile mark? B. Estimate the miles of highway with a speed limit of $30 \mathrm{mph}$ C. Evaluate $f(5), f(13),$ and $f(19)$ D. At what $x$ -values is the graph discontinuous? Interpret each discontinuity.

Use the graphs to answer each item. Do not use a calculator.
The graph of $y=f(x)$ gives the speed limit $y$ along a rural highway after traveling $x$ miles.
(GRAPH NOT COPY)
A. What is the speed limit at the 4 -mile mark?
B. Estimate the miles of highway with a speed limit of $30 \mathrm{mph}$
C. Evaluate $f(5), f(13),$ and $f(19)$
D. At what $x$ -values is the graph discontinuous? Interpret each discontinuity.

Key Concepts

Graph Interpretation

This concept involves understanding and reading data from a visual representation of a function. It includes identifying key points such as the value of the function at specific inputs, the behavior of the function over intervals, and the general trends displayed in the graph. Mastery of graph interpretation is essential for extracting accurate information from visual data representations.

Function Evaluation

Function evaluation is the process of finding the output of a function for a given input. When presented with a graph, this involves locating the input value along the x-axis and reading the corresponding y-value on the graph. This is a fundamental skill for understanding how functions behave and for determining the value of a function at specific points.

Estimation from Graphical Data

Estimation from graphs refers to the practice of approximating values when exact data points are not explicitly provided. This includes determining intervals over which a function meets certain criteria or approximating the function's output between known data points. It is crucial when the graph does not provide exact numerical labels or when a calculator is not used.

Discontinuities in Graphs

Discontinuities are points or intervals where a function is not continuous, meaning there is a break or jump in the graph. Understanding discontinuities involves identifying where these breaks occur and interpreting their significance in the context of the function's behavior. This might include recognizing jump discontinuities, removable discontinuities, or asymptotic behavior, which indicate sudden changes in the function’s value or behavior.

Transcript

00:01 All right, so i did my best to copy the graph that was given in the book.

00:05 We have our x -axis which is going to be our distance and then the y -axis is your speed limit.

00:15 So we're going to use this graph to answer the four questions given.

00:20 So first question, a.

00:22 What is the speed limit at the four mile mark? that means we have to look up from four and you'll see that there are two points that that x equals four line goes through but this top one is an open circle versus this one which is a closed circle.

00:42 The closed circle is the one that the graph actually exists at at that point so we know that the speed limit at the four mile mark is going to be 40 miles per hour.

00:54 Looking at the next question, a.

00:58 Estimate the miles of highway with a speed limit of 30.

01:01 So there are two chunks that have 30.

01:04 We have this and we have this.

01:08 So it looks like from about mile six up to mile eight.

01:19 Now it doesn't include mile eight because of that open circle but right up to it and then it's going to start up again at mile 12 up to mile 16 because those are the two places where that graph equals 30.

01:36 All right the next one has us making some estimations or evaluating.

01:43 F is 5, f is 13, and f is 19.

01:49 So just like we did in the first one we're just going to go to those places on the x -axis and then look up to see where the graph exists.

01:58 So f of 5 would be about here.

02:02 So if we go up looks like it is going to equal 40.

02:07 So 40 miles per hour there.

02:10 13 would be about here.

02:12 So if we go up we see that we equal 30 miles per hour there...