Note that different Java implementations will compute and report different accuracies, so the values you find may may be slightly different from those above. The points in the table show that the real minimum point has an x coordinate somewhere between 1. Note that we do not yet have enough information to report the x value with even one decimal place accuracy, because if the second decimal place were a 4, then the value would round to 1.
If the second decimal place were a 7, then the value would round to 1. So we need to improve our estimate by zooming in on the minimum point.
There are several ways to do this with the Grapher : Zoom In , Zoom Box , or set the coordinates of the viewing rectangle.
In this example we will set the view coordinates. Changing the viewing rectangle removes the trace point. To get it back, click the Trace button again. Now you need to move left to get to the minimum point. There are two different x values that correspond to the lowest y value. We still do not know the exact location of the minimum point, but we know that its x coordinate is between 1.
That means the x coordinate will be 1. Since we are only reporting three decimal places for the x coordinate, we will also round the y coordinate to three decimal places, so our approximation is 1. Find the relative maximum point to two decimal place accuracy. A function f is even if its graph is symmetric with respect to the y-axis. For example, if you evaluate f at 3 and at -3, then you will get the same value if f is even.
This function is not even, so when we graph its reflection about the y-axis, we will get a new graph. In the g text box type f -x , and click the Graph button The graph of g is the reflection about the y-axis of the graph of f. Since we see two distinct graphs, we know that f is not even. This graph is symmetric with respect to the y-axis, so when you enter f -x in the g box and graph again, you do not see anything new.
If a graph passes the vertical line test then it is a function. What I mean by that is if you move your pen and it hits only once then yes it's a function, if it hits more than once, no it's not a function.
I personally kind of like theses problems I think they are not too hard and there is no numbers involved so that's kind of cool. All Algebra videos Unit Graphs and Functions. Previous Unit Absolute Value. Alissa Fong. Thank you for watching the video. Start Your Free Trial Learn more. Explanation Transcript Use the vertical line test to determine whether or not a graph represents a function.
We will see these toolkit functions, combinations of toolkit functions, their graphs, and their transformations frequently throughout this book.
It will be very helpful if we can recognize these toolkit functions and their features quickly by name, formula, graph, and basic table properties. The graphs and sample table values are included with each function shown below.
Improve this page Learn More. Skip to main content. Module 5: Function Basics. Search for:. Identify Functions Using Graphs Learning Outcomes Verify a function using the vertical line test Verify a one-to-one function with the horizontal line test Identify the graphs of the toolkit functions.
How To: Given a graph, use the vertical line test to determine if the graph represents a function. Inspect the graph to see if any vertical line drawn would intersect the curve more than once.
If there is any such line, the graph does not represent a function. If no vertical line can intersect the curve more than once, the graph does represent a function. Both an equation and a function can define a curve on the plane, but some equations do not have an associated function. Mike B. Sign up or log in Sign up using Google. Sign up using Facebook.
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