What is covered in Grade 11 Mathematics Functions?

Parabola, hyperbola and exponential functions: properties, transformations, asymptotes, domain and range. Composite functions.

Is Grade 11 Functions tested in Paper 1 or Paper 2?

Grade 11 Mathematics Functions is assessed in Paper 1 of the end-of-year examinations, as per the CAPS Mathematics curriculum guidelines.

When is Functions taught in Grade 11 Mathematics?

Functions is taught in Term 2 of Grade 11 according to the CAPS Annual Teaching Plan (ATP) for Mathematics in South Africa.

Is Grade 11 Mathematics Functions on the CAPS curriculum?

Yes. Functions is part of the official CAPS Mathematics curriculum for Grade 11, Term 2 in South Africa. The content on MathSciBuddy follows the Annual Teaching Plan (ATP) set by the Department of Basic Education.

Is this Grade 11 Mathematics study material free?

Yes. All chapter notes, definitions, formulas, and worked examples on MathSciBuddy are completely free to read. No account or subscription is needed to access CAPS-aligned study notes.

Grade 11 Mathematics

Grade 11 · Term 2Mathematics

Functions

We extend the study of functions to include horizontal and vertical shifts of all four function families, inverses of functions, and the logarithmic function.

Week 3

5.1 Transformations & Inverses of Functions

Sketch $y=a(x+p)^2+q$ (parabola with vertex shift)
Apply horizontal and vertical shifts to all function families
Determine and sketch the inverse of a function; restrict domain for inverse to be a function

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Real-World Connection

Every digital filter applied to a photo (brightness, contrast, zoom) is a transformation of a function. The inverse transformation returns the photo to its original state — proving that if you understand inverses, you can 'undo' any transformation.

Property / Rule

Parabola $y=a(x+p)^2+q$

The vertex (turning point) is at $(-p, q)$ . The axis of symmetry is $x=-p$ . The $a$ value determines the direction and width of opening.

\text{TP: }(-p,q);\quad\text{AoS: }x=-p

Property / Rule

Inverse of a Function

The inverse $f^{-1}$ swaps inputs and outputs. Graphically, the inverse is the reflection of $f$ in the line $y=x$ . To find the equation: swap $x$ and $y$ , then solve for $y$ .

\text{If }f(a)=b\text{ then }f^{-1}(b)=a

Property / Rule

Restricting the Domain

If $f$ is not one-to-one (e.g. a parabola), the full inverse is not a function. Restrict the domain of $f$ (e.g. $x\geq0$ ) so that the inverse IS a function.

f(x)=x^2,\;x\geq0\Rightarrow f^{-1}(x)=\sqrt{x}

ℹ️ Note

The domain of $f^{-1}$ is the range of $f$ , and vice versa. This is a useful shortcut for reading off the range of an inverse.

Worked Examples

Worked Example

Parabola in vertex form

Problem

f(x) = -2(x+3)^2+8

Worked Example

Find and sketch the inverse

Problem

f^{-1}

Activity — 8 Questions

CAPS Cognitive Level Distribution

L1 · Knowledge2 Q

L2 · Routine Procedures2 Q

L3 · Complex Procedures2 Q

L4 · Problem Solving2 Q

L1 · Knowledge2 marks

State the vertex of

y=3(x-1)^2-5

L1 · Knowledge2 marks

Find

f^{-1}

f(x)=x-4

L2 · Routine Procedures3 marks

Find

x

-intercepts of

y=(x+2)^2-9

L2 · Routine Procedures3 marks

Find

f^{-1}

for

f(x)=3x-6

and evaluate

f^{-1}(9)

L3 · Complex Procedures4 marks

For

f(x)=x^2-4

with

x\geq0

, find and sketch

f^{-1}

L3 · Complex Procedures5 marks

The parabola

y=a(x+p)^2+q

has

x

-intercepts

-1

and

3

, and passes through

(0,-3)

. Find

a

p

q

L4 · Problem Solving4 marks

f(x)=\frac{2}{x}+1

(for

x>0

), find

f^{-1}

and state its domain.

L4 · Problem Solving3 marks

Show that

f(f^{-1}(x))=x

for

f(x)=3x+2

Analytical Geometry

Finance, Growth & Decay