EVALUATING PIECEWISE FRUNCTIONS FROM A GRAPH

Let us consider the following,

f(a) = b

here a is input and b is output.

• Along the x-axis find the input, draw the vertical line through this point.
• The vertical line where it cuts the curve is known as output (y-value).
• If we see the transparent circle, we have to understand there is no curve. So, it will give undefined output.
• If we see the solid circle, we have to understand there is  curve. So, we can mark the y-value.

Evaluate the following from the graph.

Problem 1 :

 (i)  𝑓(2) =(ii)  𝑓(−3) =(iii)  𝑓(−1) =(v)  𝑓(−4) =

Solution :

Problem 2 :

Evaluate

(i)  𝑓(0) =    (ii)  𝑓(−4) =     (iii)  𝑓(−1) =      (iv)  𝑓(3) =

Solution :

(i)  𝑓(0) = 2

(ii)  𝑓(−4) = 1

(iii)  𝑓(−1) = -2

(iv)  𝑓(3) = 3

Problem 3 :

Evaluate the following :

a) 𝑓(−1) =     b) 𝑓(2) =   c) 𝑓(1) =   d) 𝑓(−2) =     e) f(0) =

Solution :

a) 𝑓(−1) =  0

b) 𝑓(2) =  1

c) 𝑓(1) =  1

d) 𝑓(−2) = -1

e) f(0) = 1

Problem 4 :

Evaluate the following :

𝑎. 𝑓(−3) =      b. 𝑓(4) =     c. 𝑓(1) =    d. 𝑓(−1) =    e. 𝑓(0) =

Solution :

𝑎. 𝑓(−3) =  -3

b. 𝑓(4) =  4

c. 𝑓(1) =  1

d. 𝑓(−1) =  undefined

e. 𝑓(0) = 1

Problem 5 :

Evaluate the following :

𝑎. 𝑓(3) =   b. 𝑓(−1) =    c. 𝑓(−3) =     d. 𝑓(2) =     e. 𝑓(0.5) =

Solution :

𝑎. 𝑓(3) = 2

b. 𝑓(−1) =  undefined

c. 𝑓(−3) = 3

d. 𝑓(2) = 1

e. 𝑓(0.5) = 2.5

Problem 6 :

Evaluate the following :

𝑎. 𝑓(−4) =   b. 𝑓(1) =     c. 𝑓(3) =     d. 𝑓(2) =      e. 𝑓(1.5) =

Solution :

𝑎. 𝑓(−4) = 0

b. 𝑓(1) = 1

c. 𝑓(3) = 0

d. 𝑓(2) =  1

e. 𝑓(1.5) = -2

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