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)
