The graph below shows the relationship between the number of hours and the number of miles jogged.
Y
16
15
14
13
12
11
10
9
Miles
8
3
2
2
3
5
6
Hours
Based on the information in the graph, what is the unit rate in miles per hour?

1. In a function, every output value corresponds to exactly one input value

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

This is the correct statement:

In a function, every input value corresponds to exactly one output 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 NOT a function.

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

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 first figure attached

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

In the second figure attached 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 every time passed there is a height of the ball. Remember: every input value corresponds to exactly one output value

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 every grade level maybe there are different height values (more than one value). Remember: every input value corresponds to exactly one output value.

6. Complete the sentences:

6a. The x-intercept of a graph is the location where the graph crosses the x-axis

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

6c. The x-coordinate of the y-intercept is always zero

6d. The y-coordinate of the x-intercept is always zero

6e. The x-intercept is the solution 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 the point where the graph of this function crosses the y-axis. 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 the point where the graph of this function crosses the y-axis.

This means this curve crosses the y-axis in the point (0,0), also called The origin 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)