Reviewed by Janice S. Armas
Which input value produces the same output for the two functions on the graph? x = -3, x = -2, x = -1, x = 3
Answer: x = -1 produces the same output for the two functions on the graph
In mathematics, two functions produce the same output at an input value x if their graphs intersect at that point. To determine which value of x results in the same output for both functions, we look for points of intersection on the graph where the y-values for both functions are equal.
Methods
Math Tutor Explanation Using Graph Analysis Method
By examining the graph, you can visually identify where the two functions meet and determine the x-value at which their outputs are the same.
Step 1: Step 1: Locate the points where the two function graphs intersect
Step 2: Step 2: Read the x-coordinate at the intersection point(s)
Math Tutor Explanation Using Table of Values Method
If the graph is not available, you could make a quick table of values for each function and check at which input value the outputs are equal.
Step 1: Step 1: Calculate or find the output of each function for x = -3, x = -2, x = -1, and x = 3
Step 2: Step 2: Compare the output values for each x
Step 1:
Step 2:
Math Tutor suggests: Practice Matching Function Outputs on Graphs
Explore more questions about comparing functions and analyzing graphs to further solidify your understanding.
FAQ on Intersection Points of Functions
What does it mean when two functions have the same output?
It means their graphs intersect at that x-value, having equal y-values.
Can two functions have more than one point where their outputs are the same?
Yes, two functions can intersect at multiple x-values.
How do I find the intersection point algebraically?
Set the two function expressions equal to each other and solve for x.
What if the intersection point is not listed as an option?
That means none of the provided x-values produce the same output for both functions.
How do I read intersection points on a graph?
Find where the two curves cross and record the corresponding x-coordinate.
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