To find \( f(3) \) using a graph of the function \( f(x) \), follow these simple steps:
-
Understand what \( f(3) \) means: The notation \( f(3) \) refers to the output value of the function \( f \) when the input (or \( x \)-value) is 3.
-
Look at the graph: Find the graph of the function \( f(x) \). This graph will show a curve or a line that represents how \( f(x) \) changes as \( x \) changes.
-
Locate \( x = 3 \): Go along the horizontal axis, which is often labeled as the \( x \)-axis. Find the point where \( x \) equals 3. You can do this by moving to the right from the origin (where \( x = 0 \)) to the point where \( x = 3 \).
-
Find the corresponding \( y \)-value: From the point where \( x = 3 \), look straight up or down to find where the graph intersects that vertical line. The point where the graph meets this vertical line gives you the \( y \)-value at \( x = 3 \).
-
Read off the output value: The \( y \)-value at the point where you found the intersection is \( f(3) \). This is your answer.
For example, if the graph shows that at \( x = 3 \), the \( y \)-value is 5, then \( f(3) = 5 \).
That's it! You've used the graph to find \( f(3) \).