GRADE 11 PRECALCULUS REVIEWER
Complete Study Guide • Formulas • Examples • Practice
TABLE OF CONTENTS
Functions
● Polynomial Functions
● Rational Functions
● Exponential Functions
● Logarithmic Functions
● Trigonometric Functions
● Unit Circle
● Trigonometric Identities
● Trigonometric Equations
● Law of Sines and Law of Cosines
● Sequences and Series
● Practice Test
● Answer Key
● Quick Formula Sheet
1. FUNCTIONS
A function is a relation where every input has exactly one output.
Function Notation
A function can be written as:
f(x) = 2x + 3
To evaluate the function, substitute the given value of x.
Example:
If f(x) = 2x + 3, find f(4).
f(4) = 2(4) + 3
f(4) = 8 + 3
f(4) = 11
Important Terms :
Domain – the set of possible input values.
Range – the set of possible output values.
x-intercept – where the graph crosses the x-axis.
y-intercept – where the graph crosses the y-axis.
2. POLYNOMIAL FUNCTIONS
A polynomial function has the general form:
f(x) = aₙxⁿ + ... + a₂x² + a₁x + a₀
The degree is the highest exponent of x.
Example
f(x) = 3x⁴ − 2x² + 5
The degree is 4.
, GRADE 11 PRECALCULUS REVIEWER
Complete Study Guide • Formulas • Examples • Practice
Important Concepts
Degree
Leading coefficient
Zeros or roots
x-intercepts
y-intercept
End behavior
Factoring
Factoring Example
Solve:
x² − 5x + 6 = 0
Factor:
(x − 2)(x − 3) = 0
Therefore:
x = 2 or x = 3
3. RATIONAL FUNCTIONS
A rational function is a function written as a fraction of two polynomials.
f(x) = P(x) / Q(x)
The denominator cannot equal zero.
Example
f(x) = 1/(x − 2)
Since the denominator cannot be zero:
x−2≠0
Therefore:
x≠2
The domain is all real numbers except 2.
Key Terms
Vertical asymptote – a vertical line that the graph approaches.
Horizontal asymptote – a horizontal line that describes the graph's behavior as x becomes very
large or very small.
4. EXPONENTIAL FUNCTIONS
An exponential function has the form:
f(x) = abˣ
where a ≠ 0, b > 0, and b ≠ 1.
Exponential Growth
If:
b>1
Complete Study Guide • Formulas • Examples • Practice
TABLE OF CONTENTS
Functions
● Polynomial Functions
● Rational Functions
● Exponential Functions
● Logarithmic Functions
● Trigonometric Functions
● Unit Circle
● Trigonometric Identities
● Trigonometric Equations
● Law of Sines and Law of Cosines
● Sequences and Series
● Practice Test
● Answer Key
● Quick Formula Sheet
1. FUNCTIONS
A function is a relation where every input has exactly one output.
Function Notation
A function can be written as:
f(x) = 2x + 3
To evaluate the function, substitute the given value of x.
Example:
If f(x) = 2x + 3, find f(4).
f(4) = 2(4) + 3
f(4) = 8 + 3
f(4) = 11
Important Terms :
Domain – the set of possible input values.
Range – the set of possible output values.
x-intercept – where the graph crosses the x-axis.
y-intercept – where the graph crosses the y-axis.
2. POLYNOMIAL FUNCTIONS
A polynomial function has the general form:
f(x) = aₙxⁿ + ... + a₂x² + a₁x + a₀
The degree is the highest exponent of x.
Example
f(x) = 3x⁴ − 2x² + 5
The degree is 4.
, GRADE 11 PRECALCULUS REVIEWER
Complete Study Guide • Formulas • Examples • Practice
Important Concepts
Degree
Leading coefficient
Zeros or roots
x-intercepts
y-intercept
End behavior
Factoring
Factoring Example
Solve:
x² − 5x + 6 = 0
Factor:
(x − 2)(x − 3) = 0
Therefore:
x = 2 or x = 3
3. RATIONAL FUNCTIONS
A rational function is a function written as a fraction of two polynomials.
f(x) = P(x) / Q(x)
The denominator cannot equal zero.
Example
f(x) = 1/(x − 2)
Since the denominator cannot be zero:
x−2≠0
Therefore:
x≠2
The domain is all real numbers except 2.
Key Terms
Vertical asymptote – a vertical line that the graph approaches.
Horizontal asymptote – a horizontal line that describes the graph's behavior as x becomes very
large or very small.
4. EXPONENTIAL FUNCTIONS
An exponential function has the form:
f(x) = abˣ
where a ≠ 0, b > 0, and b ≠ 1.
Exponential Growth
If:
b>1
