EVALUATING FUNCTIONS FROM A GRAPH

Example 1 :

Given the graph of the function, find the  following values:

(i)  f(-1)  =  _____

(ii)  f(1)  =  _____

(iii)  f(3)  =  _____

(iv)  x when f(x)  =  -4

Solution :

(i)  Trace -1 on the curve.

The curve passes through the point (-1, 0). So, the value of f(-1) is 0.

(ii)  Trace 1 on the curve, the curve passes through the point (1, -1). So, the value of f(1) is -1.

(iii)  Trace 3 on the curve, the curve passes through the point (3, 2). So the value of f(3) is 2.

(iv)  Trace -4 on y-axis. Left side of -4 on the y-axis, we have part of the curve, we can trace the point (-4, -4) on the curve.

So, the value of x is -4, when f(x)  =  -4.

Example 2 :

Given the graph of the function, find the following values:

(i)  f(4)  =  _____

(ii)  f(8)  =  _____

(iii)  f(6)  =  _____

(iv)  x when f(x)  =  2

Solution :

From the above graph,

(i)  f(4)  =  4

(ii)  f(8)  =  6

(iii)  f(6)  =  5

(iv)  By observing 2 on the y-axis, the curve crosses the y-axis at the point (0, 2).

So, the value of x is 0, when f(x)  =  2.

Example 3 :

Given the graph of the function, find the following values:

(i)  g(-4)  =  _____

(ii)  f(8)  =  _____

(iii)  g(f(2))  =  _____

(iv)  h(-1)  =  _____

(v)  h(2)  =  ______

Solution :

(i)  On the curve g(x), straight to -4, we have 1. So, the value of g(-4) is 1.

(ii)  f(8). In the curve f(x), we don't have continuity of the curve after 8. So, value of f(8) is does not exists.

(iii)  g(f(2)) :

First let us evaluate f(2), by observing the graph the value of f(2) is 1.

g(f(2))  =  g(1)

We don't have continuity of curve near 1. So, it does not exists.

(iv)  h(-1)

Straight to -1 on the curve, we have the point -3.

So, the value h(-1) is -3.

(v)  By observing the graph, the value of h(2) is -3.

Example 4 :

Given the graph of the function, find the following values:

(i)  g(7)  =  ____

(ii)  g(0) + f(3)  =  ____

(iii)  f(g(7))  =  _____

(iv)  g(f(8))  =  _____

(v)  Find x if f(x) = 2

Solution :

By observing the graph,

(i)  g(7)  =  6

(ii)  g(0) + f(3) 

 g(0)  =  6 and f(3)  =  (-1)

g(0) + f(3)   =  6-1  ==>  5

(iii)  f(g(7)) 

First evaluate g(7). 

g(7)  =  6

f(g(7))  =  f(6)  ==>  1

(iv)  g(f(8))

First evaluate f(8). 

f(8)  =  1

g(f(8))  =  g(1)  ==>  6

(v)  Find x if f(x) = 2

When x =  -7, we get the value of f(x) as 2.

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