If f(x) is an even function and (6, 8) is one the points on the graph of f(x), which reason explains why (–6, 8) must also be a point on the graph?
Mathematics · High School · Tue Nov 03 2020
Answered on
The definition of an even function is that for every x in the function's domain, f(x) = f(-x). This means that an even function is symmetric with respect to the y-axis. In other words, for any given point (a, b) on the graph of an even function, the point (-a, b) will also be on the graph.
Given that (6, 8) is a point on the graph of f(x), and f(x) is an even function, we can use the definition of an even function to find another point on the graph. If we plug in x = 6 into the definition, we get f(6) = f(-6). Since (6, 8) is on the graph, we know that f(6) = 8. Therefore, f(-6) must also be equal to 8. So the point (-6, 8) must be on the graph of f(x) because f(x) is even, which ensures symmetrical points around the y-axis.