**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.

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" ?

**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.

**Answer :**

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 k 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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