# FUNCTION NOTATION AND EVALUATING FUNCTIONS WORKSHEET

## About "Function notation and evaluating functions worksheet"

Function notation and evaluating functions worksheet :

Worksheet on function notation and evaluating functions is much useful to the students who would like to practice problems on functions.

## Function notation and evaluating functions worksheet - Problems

1.  Write the equation given below as a function of "x"

2x + 3y - 5  =  0

2.  Evaluate f(4) where f(x)  =  3(2x+1)

3.  Evaluate f(w+2) where f(x) = x² + 3x + 5

4.  Evaluate f(3) where f(m)  =  (2m² + 5m - 7) / 2.

5.  Given f  =  x² - x - 4, if f(k)  =  8, what is the value of "k" ?

## Function notation and evaluating functions worksheet - Solution

Problem 1 :

Write the equation given below as a function of "x"

2x + 3y - 5  =  0

Solution :

To write the given equation as a function of "x", define the given equation by "y" in terms of "x"

2x + 3y - 5  =  0

Take -2x and +5 on both sides

(2x + 3y - 5) - 2x + 5  =  -2x + 5

3y  =  5 - 2x

Divide both sides by 3

3y/3  =  (5 - 2x)/3

y  =  (5 - 2x)/3

Let y  =  f(x)

f(x)  =  (5 - 3x)/3

Problem 2 :

Evaluate f(4) where f(x)  =  3(2x+1)

Solution :

To evaluate f(4), we have to plug x = 4 in f(x).

Then, we have

f(4)  =  3[2(4) + 1]

f(4)  =  3[8 + 1]

f(4)  =  3 x 9

f(4)  =  27

Problem 3 :

Evaluate f(w+2) where f(x) = x² + 3x + 5

Solution :

To evaluate f(w+2), we have to plug x = w in f(x).

Then, we have

f(w+2)  =  (w+2)² + 3(w+2) + 5

f(w+2)  =  w² + 2² + 2w(2) + 3w + 6 + 5

f(w+2)  =  w² + 4 + 4w + 3w + 6 + 5

f(w+2)  =  w² + 7w + 15

Problem 4 :

Evaluate f(3) where f(m)  =  (2m² + 5m - 7) / 2.

To evaluate f(3), we have to plug m = 3 in f(m).

Then, we have

f(3)  =  [2(3)² + 5(3) - 7] / 2

f(3)  =  [18 + 15 - 7 ] / 2

f(3)  =  26 / 2

f(3)  =  13

Problem 5 :

Given f  =  x² - x - 4, if f(k)  =  8, what is the value of "k" ?

Solution :

Set the function rule to 8 and solve for "k".

Then, we have

x² - x - 4  =  8

Subtract 8 on both sides

(x² - x - 4) - 8  =  8 - 8

x² - x - 12  =  0

(x + 3)(x - 4)  =  0

x + 3 =0 ; x - 4 = 0

x  =  -3 ; x  =  4

Hence, the value of can be either 4 or -3.

After having gone through the stuff given above, we hope that the students would have understood "Worksheet on function notation and evaluating functions".

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