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Lera25 [3.4K]
2 years ago
15

Could you help me on this? i dont think i have the right anwsers

Mathematics
1 answer:
Step2247 [10]2 years ago
6 0
<h2><u>Answers: </u></h2>

1. <em>In a function, every output value corresponds to exactly one input value</em>


This is false, because <u>the definition of a function</u><u> states that each input value (domain) must have one output value (range).</u> Then, in this statement the words that need to be changed are <u>output</u> and <u>input. </u>

This is the correct statement:


In a function, every <u>input</u> value corresponds to exactly one <u>output</u> value



2a. Explain how the vertical line test shows that this relation is not a function:


The vertical line test consists in drawing a vertical line over the traced curve, if this line cuts the curve in two points or more, this is automatically <u>NOT a function</u>.


In this case, if we trace a vertical line in the graph shown, <u>the line cuts the graph in two points</u>



2b. Name two points on the graph that show that this relation is NOT a function:


According to the graph shown, two points would be (4,2) and (4,-2)



3. Sketch the graph of a relation that is a function:


The curve traced in the archive attached is ok if we want to show a relation that is a function.

Another example could be the shown in the <u>first figure attached</u>


4. Sketch the graph of a relation that is NOT a function:


In <u>the second figure attached</u> is shown the graph of a circle, where we can clearly see it fails the vertical line test.


 

5. Determine if each one represents a function or not:


5a. A golf ball is hit down a fairway. The golfer relates the time passed to the height of the ball


Function

In this case, for <u>every time passed</u> there is a <u>height of the ball</u>. <em>Remember: every input value corresponds to exactly one output value</em>


5b. A trainer takes a survey at all the athletes in a school about their height, rounded to the nearest inch, and their grade level. The trainer relates their grade levels to their heights.


Not a Function

In this case, for <u>every grade level</u> maybe <u>there are different height values (more than one value)</u>. <em>Remember: every input value corresponds to exactly one output value.</em>

6. Complete the sentences:


6a. The <u>x-intercept</u> of a graph is the location where the graph crosses the x-axis


6b. The <u>y-intercept</u> of a graph is the location where the graph crosses the y-axis


6c. The <u>x-coordinate</u> of the y-intercept is always zero


6d. The <u>y-coordinate</u> of the x-intercept is always zero


6e. The x-intercept is the <u>solution</u> of a function or group



7a. The above graph is linear


7b. Is the above graph a function?


Yes, if you do the vertical line test, the line cuts or intercepts only one point.


7c. The y-intercept is the point (0,10) and represents <u>the point where the graph of this function crosses the y-axis</u>. This means this curve crosses the y-axis in the point (0,10)



7d. Why would there not be an x-intercept for this situation?


Because in the figure is not shown the point in which the line crosses the x-axis. Nevertheless, this line should have an x-intercept, but is not shown here.


If a line has no x-intercept, this means it must be parallel to the x-axis (never crosses it), but in this case this line does not seem to be parallel to the x-axis.

This line have an x-intercept in the negative part of the x-axis


8a. The above graph is non-linear


8b. Yes it is a function, if you do the vertical line test, it will cut the curve in one point


8c. The y-intercept is 0 (point (0,0)), and represents <u>the point where the graph of this function crosses the y-axis</u>.

This means this curve crosses the y-axis in the point (0,0), also called <u>The origin</u> of the coordinate system. This is also one of th x-intercepts of this graph.


8d. What is the solution to this graph and what does it represent in this situation?


This a negative vertical parabola, represented by the quadratic equation. The solutions are the x-intercepts which are the points (0,0) and (100,0)




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