FUNCTION NOTATION AND EVALUATING FUNCTIONS WORKSHEET

Questions 1-4 : Write the given equation as a function of x.

Question 1 :

2x + 3y - 5  =  0

Question 2 :

x²y + 3xy - 3 = 0

Question 3 :

log₁₀y = x

Question 4 :

log(x) + log(y) = log (x + y)

Question 5 :

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

Question 6 :

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

Question 7 :

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

Question 8 :

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

1. Answer :

2x + 3y - 5 = 0

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

2x + 3y - 5 = 0

Subtract 2x and 5 from both sides.

3y = 5 - 2x

Divide both sides by 3.

y = (5 - 2x)/3

y = (5 - 2x)/3

Let y = f(x).

f(x) = (5 - 3x)/3

2. Answer :

x²y + 3xy - 3 = 0

Add 3 to both sides.

x²y + 3xy = 3

y(x² + 3x) = 3

Divide both sides by (x² + 3x).

y = 3/(x² + 3x)

3. Answer :

log₁₀y = x

Convert the equation to exponential.

y = 10^x

Let y = f(x).

f(x) = 10^x

4. Answer :

log(x) + log(y) = log(x + y)

log(xy) = log(x + y)

xy = x + y

Subtract y from both sides.

xy - y = x

y(x - 1) = x

Divide both sides by (x - 1).

y = x/(x - 1)

Let y = f(x).

f(x) = x/(x - 1)

5. Answer :

f(x) = 3(2x + 1)

Substitute x = 4. 

f(4) = 3[2(4) + 1]

= 3[8 + 1]

= 3(9)

= 27

6. Answer :

f(x) = x² + 3x + 5

Substitute x = w + 2.

f(w + 2) = (w + 2)² + 3(w + 2) + 5

= (w + 2)(w + 2) + 3w + 6 + 5

= w² + 2w + 2w + 4 + 3w + 6 + 5

= w² + 7w + 15

7. Answer :

f(m) = (2m² + 5m - 7)/2

Substitute m = 3.

f(3) = [2(3)² + 5(3) - 7]/2

= [2(9) + 15 - 7 ]/2

= (18 + 15 - 7)/2

= 26/2

= 13

8. Answer :

f(k) = 8

k² - k - 4 = 8

Subtract 8 from both sides.

k² - k - 12 = 0

factor and solve.

(k + 3)(x - 4) = 0

k + 3 = 0   or   k - 4 = 0

k = -3   or   k = 4

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.