Skills Checklist | IB Math AASL

Skill Checklist

Track your progress across all skills in your objective. Mark your confidence level and identify areas to focus on.

9 Skills Available

Track your progress:

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📖 = included in formula booklet • 🚫 = not in formula booklet

Track your progress:

Don't know

Working on it

Confident

📖 = included in formula booklet • 🚫 = not in formula booklet

Linear Transformations

7 skills

Vertical translation of graphs y=f(x)+b

SL 2.11

The graph of y=f(x)+b can be obtained from the graph of y=f(x) by a vertical translation b units upwards (if b<0, the transformation may also be called a translation ∣b∣ units down).

Horizontal translation

SL 2.11

The graph of y=f(x−a) can be obtained from the graph of y=f(x) by a horizontal translation a units to the right (if a<0, the transormation may also be called a translation ∣a∣ units to the left).

Translation by a vector

SL 2.11

If a point P is translated by a vector (ab), apply a translation a units to the right and b units up:

P(x,y)P′(x+a,y+b).

Vertical scaling of graphs y=af(x)

SL 2.11

The graph of y=pf(x) can be obtained from the graph of y=f(x) by a vertical stretch with scale factor p.

Horizontal scaling

SL 2.11

The graph of y=f(qx) can be obtained from the graph of y=f(x) by a horizontal stretch with scale factor q1.

Reflection in the x-axis

SL 2.11

The graph of y=−f(x) can be obtained from the graph of y=f(x) by a reflection in the x-axis.

Reflection in the y-axis

SL 2.11

The graph of y=f(−x) can be obtained from the graph of y=f(x) by a reflection in the y-axis.

Rational functions

2 skills

The reciprocal function 1/x

SL AA 2.8

The reciprocal function is defined by f(x)=x1.

Notice that f(x) is not defined for x=0. In fact, since x1 gets very large as x approaches 0, f(x) has a vertical asymptote at x=0.

And since for very large x, x1 approaches zero, there is also a horizontal asymptote y=0.

Notice also that x11=x, so f(x)=x1 is self-inverse.

Graphs of linear rational functions

SL AA 2.8

A linear rational function has the form

f(x)=cx+dax+b

When the denominator is zero the graph will have a vertical asymptote:

cx+d=0⇒x=−cd🚫

And as x gets very large, the +b and +d can be ignored:

y=f(x)≈cxax=ca🚫

So there is a horizontal asymptote at y=ca.