5 Problems - SHOW ALL WORK!
1. How can we determine from a graph if a function is shown or not?
2. How can you tell from a table of values if the relationship is a function or not?
3. How can you tell from an equation is the relationship is a function?
4. Is the number of students on a field trip a function of the number of buses used? Explain.
5. Is the time it takes you to run a 100-meter race a function of the speed you run? Explain.
What do I need help with?
1. To determine if a function is shown on a graph, we need to check if there is a unique output for every input value. This can be done by using the vertical line test. If a vertical line can intersect the graph in more than one point, then it does not represent a function.
2. From a table of values, we can determine if the relationship is a function by checking if there is a unique output for every input value. If there are multiple output values for a single input value, then it does not represent a function.
3. From an equation, we can determine if the relationship is a function by checking if there is a unique output for every input value. We can do this by solving for the dependent variable (output) in terms of the independent variable (input) and checking if there are any values of the input that result in multiple output values.
4. The number of students on a field trip is not necessarily a function of the number of buses used. It is possible to have multiple numbers of students for a given number of buses, such as if there are different student populations being transported by different buses.
5. The time it takes to run a 100-meter race is not a function of the speed you run. Multiple runners can have the same speed and finish the race in different times, or a runner can have different speeds at different points in the race. Therefore, there is not a unique output for every input value (speed), so it does not represent a function.