Home / IB DP Maths / Analysis and Approach HL / MAA HL Flashcards / IB Mathematics AA HL Flashcards- Key features of graphs

IB Mathematics AA HL Flashcards- Key features of graphs

[qdeck ” ]

[h] IB Mathematics AA HL Flashcards- Key features of graphs

[q] Key features of graphs

[a]

You may well be asked to draw or sketch the graphs of functions. Drawing should be as accurate as possible, including all relevant graph features. Sketching should just give a general idea of the shape, with some features, depending on how the question is phrased, and what type of function is asked for.

[q]

FEATURES
Here we can define the main types of graph features:

– Maximum/Minimum values: ‘Turning points’ of the graph: max or min.

– Intercepts: Where the graph crosses the x-axis or the y-axis.

– Line of symmetry: Mainly regarding quadratics, self-explanatory.

[a]

– Vertex: Max. or min. points for quadratic function.

– Zeros, Roots: Where \(y = 0\), i.e.: the x-intercepts.

– Asymptotes: A line that a graph will get infinitely close to but will never touch, as the x or y tends to infinity.

– Intersection points: The point where two lines cross (intersect).

[q]
FEATURES ON A GRAPH
To visualize the above features:

[a]
GDC
To graph almost any function, we press:

– TI-nspire →
\( \boxed{B: \text{GRAPH}} \) → \( \boxed{\text{TAB}} \) → type function → \( \boxed{\text{ENTER}} \)

– TI-84 →
\( \boxed{Y=} \) → type function → \( \boxed{\text{GRAPH}} \)

[q]

FINDING FEATURES w/GDC ➔ You can find the features previously defined by using your GDC’s ‘analyse graph’ capabilities:

TI-nspire ➔ MENU ➔ 6: ANALYSE GRAPH… // TI-84 ➔ 2ND ➔ CALC

[a]

FINDING FEATURES ➔ We can find many of these manually:

– Turning Points ➔ You can use calculus (see topic 5), or for quadratics, you can use \(x = \frac{-b}{2a}\) (see 2.6 for A&A, 2.5 for A&I), otherwise use a GDC.
– Intercepts ➔ To be on the y-axis, you must have \(x = 0\), so if you plug in \(x = 0\) and solve for \(y\), you have the y-intercept. Reverse this for x-intercept(s).

[q]

– Zeros & Roots ➔ Again, set \(y = 0\) and solve.
– Vertical Asymptotes ➔ At an x value of restricted domain, such as the x value that means you would be dividing by 0.

[a]

– Horizontal Asymptotes ➔ To find what value the graph gets closer and closer to, we can plug in very large values for x. Or use advanced calculus (limits).
– Intersection Points ➔ See 2.7 (set functions equal to each other, and solve)

[q]

E.G. 1 ➔ Draw the graph of \(f(x) = \frac{2}{x – 1} + 1\):

– Divide by zero when \(x = 1\), so V.A. at \(x = 1\)
– As \(x \rightarrow \infty\), \(f(x) = 0 + 1 = 1\), so H.A. at \(x = 1\)
– Plug in \(x = 0\): \(f(0) = \frac{2}{0 – 1} + 1 = -1\), y-int. at \((0, -1)\)
– Set \(f(x) = 0\): \(0 = \frac{2}{x – 1} + 1 \Rightarrow x = -1\), x-int. at \((-1, 0)\)

 

 

[x] Exit text

(enter text or “Add Media”; select text to format)

[/qdeck]

IB Mathematics AA HL Flashcards- Key features of graphs

IB Mathematics AA HL Flashcards- All Topics

Scroll to Top