FIND VALUES OF FUNCTIONS FROM GRAPHS

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

Working Rule to Find Value of a Function From Its Graph

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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