MAT1512 Assignment 1 solutions 2026
University of South Africa
College of Science, Engineering and Technology
Department of Mathematical Sciences
Tutorial Letter 101/3/2026
MAT1512 – Calculus I
Assignment 01
IMPORTANT INFORMATION
, • Total Marks: 50
• Due Date: (See myUnisa)
• This assignment covers: Functions, Algebraic
Techniques, Exponential and Logarithmic
Functions, Mathematical Modelling, Sequences and
Induction.
• Show all calculations and reasoning clearly.
• No marks will be awarded for unsupported answers.
QUESTION 1
𝑥 2 − 5𝑥 + 6
𝑓(𝑥) =
𝑥2 − 4
(a) Determine the domain of 𝒇(6 marks)
The domain of a rational function excludes values that make the denominator equal to
zero.
Set the denominator equal to zero
𝑥2 − 4 = 0
Factor:
𝑥 2 − 4 = (𝑥 − 2)(𝑥 + 2)
So
(𝑥 − 2)(𝑥 + 2) = 0
Thus
University of South Africa
College of Science, Engineering and Technology
Department of Mathematical Sciences
Tutorial Letter 101/3/2026
MAT1512 – Calculus I
Assignment 01
IMPORTANT INFORMATION
, • Total Marks: 50
• Due Date: (See myUnisa)
• This assignment covers: Functions, Algebraic
Techniques, Exponential and Logarithmic
Functions, Mathematical Modelling, Sequences and
Induction.
• Show all calculations and reasoning clearly.
• No marks will be awarded for unsupported answers.
QUESTION 1
𝑥 2 − 5𝑥 + 6
𝑓(𝑥) =
𝑥2 − 4
(a) Determine the domain of 𝒇(6 marks)
The domain of a rational function excludes values that make the denominator equal to
zero.
Set the denominator equal to zero
𝑥2 − 4 = 0
Factor:
𝑥 2 − 4 = (𝑥 − 2)(𝑥 + 2)
So
(𝑥 − 2)(𝑥 + 2) = 0
Thus
