Grade 11 Functions

The parabola, hyperbola, exponential and trig graphs with shifts, and the average gradient between two points.

Gr 11 Term 2 - FunctionsTerm 2 - 4 weeks (CAPS)

Practise Functions in the app →

What gets asked

• Read the turning point, asymptotes, intercepts, domain and range from an equation.
• Describe what $a$, $p$, $q$ and $k$ each do to a graph.
• Find the equation of a graph from its features.
• Work out the average gradient of a curve across a stated pair of points.

You must be able to

• In $y=a(x+p{)}^2+q$ the turning point is $(-p;q)$ - note the sign of $p$.
• Asymptotes of $y=\frac{a}{x+p}+q$ sit at $x=-p$ and $y=q$.
• The period of $\sin kx$ is $360^{\circ }$ divided by $k$.
• Average gradient is rise over run for the pair of points named, nothing else.

Traps that cost marks

• Reading $y=(x+3{)}^2$ as a shift 3 to the right. The graph moves where $x+3=0$, which is $x=-3$: three to the LEFT.
• Letting a graph cross its asymptote. An asymptote is a fence the graph approaches - branches live in their regions.
• Averaging the two $y$-values to get an average gradient. It is a gradient: difference of $y$ over difference of $x$ between the two points.

Worked example