The graph of $y = f(x)$ is symmetric across the line $x = 5$. The graph also passes through the point $(8,-7).$ Find another point that must lie on the graph of $y = f(x).$
Since the graph of $y = f(x)$ is symmetric across the line $x=5,$ it also passes through the point $(2,-7)$ with $x$-coordinate that is $2$ units away from the line of symmetry. Therefore, the point $(2,-7)$ must also lie on the graph of $y=f(x).$
what bot said, just noting that f(5-x) = f(5+x)
among all that word jumble
To find another point that must lie on the graph of $y = f(x)$, we can use the fact that the graph is symmetric across the line $x = 5$.
Since the graph is symmetric across the line $x = 5$, any point $(a, b)$ that lies on the graph must have a corresponding point $(2 \cdot 5 - a, b)$ also lying on the graph.
We know that the point $(8, -7)$ lies on the graph of $y = f(x)$, so the corresponding point also lies on the graph.
Using the symmetry property, we can find the coordinates of the corresponding point.
The $y$-coordinate of the corresponding point will be the same as the $y$-coordinate of the given point, which is $-7$.
The $x$-coordinate of the corresponding point will be $2 \cdot 5 - 8 = 2$.
Therefore, another point that must lie on the graph of $y = f(x)$ is $(2, -7)$.
To find another point that must lie on the graph of $y = f(x),$ we need to use the given information and make use of the symmetry property.
Since the graph of $y = f(x)$ is symmetric across the line $x = 5,$ any point $(x, y)$ on the graph will have a corresponding point $(2 \cdot 5 - x, y)$ on the other side of the line $x = 5.$
Let's use the point $(8, -7)$ to find another point on the graph. The corresponding point to $(8, -7)$, which is on the other side of the line $x = 5,$ will have an $x$-coordinate of $(2 \cdot 5 - 8) = 2.$
Therefore, another point that must lie on the graph of $y = f(x)$ is $(2, -7).$