5 Problems - SHOW ALL WORK!
How can we determine from a graph if a function is shown or not?
How can you tell from a table of values if the relationship is a function or not?
How can you tell from an equation is the relationship is a function?
Is the number of students on a field trip a function of the number of buses used? Explain.
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 each input (x-value) has exactly one corresponding output (y-value). This can be done by drawing vertical lines through each x-value on the graph. If each line intersects the graph at only one point, then the graph represents a function. If there are any vertical lines that intersect the graph at more than one point, then the graph does not represent a function.
2) From a table of values, we can determine if the relationship is a function by checking if each input (x-value) has exactly one corresponding output (y-value). If there are any repeated x-values with different y-values, then the relationship is not a function. If each x-value has only one corresponding y-value, then the relationship is a function.
3) From an equation, we can determine if the relationship is a function by checking if each input (x-value) has exactly one corresponding output (y-value). If there are multiple y-values for a single x-value, then the equation does not represent a function. If each x-value has one unique y-value, then the equation represents a function.
4) The number of students on a field trip is a function of the number of buses used. This is because for each number of buses used, there will be a specific and unique number of students on the field trip. Each input (number of buses) has only one corresponding output (number of students), satisfying the definition of a function.
5) The time it takes to run a 100-meter race is not a function of the speed you run. This is because for a given speed, there can be multiple possible times it takes to run the race. If the speed is the same, the time can vary depending on factors such as fatigue or starting position. This violates the definition of a function, where each input (speed) should have only one corresponding output (time).