Let the point (x, y) be on the graph of a function f. Then, y-is the value of the function for the given value of x.
If (2, 5) is on the graph of a function f(x), then 5 is the value of f(x) at x = 2. That is,
f(2) = 5
Find the value of a function f(x) when x = a.
Step 1 :
Draw a vertical line through the value 'a' on x-axis.
Step 2 :
Mark the point of intersection of the line x = a and graph of f(x).
Step 3 :
Draw an horizontal line from the point of intersection to y-axis.
Step 4 :
Let the horizontal line meet the y-axis at 'b'.
The value of the function f(x) at x = a is 'b'.
That is,
f(a) = b
Example 1 :
Use the graph of f(x) shown below to find f(6).
Solution :
We have to find value of the function f(x) at x = 6.
Step 1 :
Draw a vertical line through 6 on the x-axis.
Step 2 :
Mark the point of intersection of the vertical line x = 6 and the graph of f(x).
Step 3 :
Draw an horizontal line from the point of intersection to y-axis.
Step 5 :
The horizontal line meets y-axis at 4.
So, the value of the function f(x) at x = 6 is 4.
That is,
f(6) = 4
Example 2 :
Use the graph of f(x) shown below to find f(9).
Solution :
We have to find value of the function f(x) at x = 9.
Step 1 :
Draw a vertical line through 9 on the x-axis.
Step 2 :
Mark the point of intersection of the vertical line x = 9 and the graph of f(x).
Step 3 :
Draw an horizontal line from the point of intersection to y-axis.
Step 5 :
The horizontal line meets y-axis at 7.
So, the value of the function f(x) at x = 9 is 7.
That is,
f(9) = 7
Example 3 :
Use the graph of f(x) shown below to find f(4).
Solution :
We have to find value of the function f(x) at x = 4.
Step 1 :
Draw a vertical line through 4 on the x-axis.
Step 2 :
Mark the point of intersection of the vertical line x = 4 and the graph of f(x).
Step 3 :
Draw an horizontal line from the point of intersection to y-axis.
Step 5 :
The horizontal line meets y-axis at 7.
So, the value of the function f(x) at x = 4 is 7.
That is,
f(4) = 7
Example 4 :
Use the graph of f(x) shown below to find f(4).
Solution :
We have to find value of the function f(x) at x = 4.
Step 1 :
Draw a vertical line through 4 on the x-axis.
Step 2 :
Mark the point of intersection of the vertical line x = 4 and the graph of f(x).
Step 3 :
Draw an horizontal line from the point of intersection to y-axis.
Step 5 :
The horizontal line meets y-axis at 5.
So, the value of the function f(x) at x = 4 is 5.
That is,
f(4) = 5
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