Read off the exact y-value for a given x - useful for checking answers and for questions that ask for a specific coordinate.
In short: Evaluating a function at a point means finding f(a) for a given value a. On a GDC you can store the function and use a table, the trace tool or the function name directly, then type the value. This avoids arithmetic slips and is the quickest way to check an answer or a coordinate on a graph.
When you'd use this
A question asks for f(a) for a specific value of a, rather than the general expression.
Checking a coordinate on a graph without reading it off by eye.
Verifying a value you calculated by substitution, especially for a messier function.
Using a regression equation to predict a value (a model is just a function).
At a glance: TI-84 Plus CE, Casio fx-CG50 and TI-Nspire CX compared
TI-84 Plus CE
Casio fx-CG50 and fx-CG100
TI-Nspire CX
Key sequence
Method 1 - Table: 2nd → GRAPH (TABLE), scroll to the x you want. Method 2 - Trace: press TRACE, then type the x-value and press ENTER. Method 3 - Home screen: type Y1(value) e.g. Y1(3) using VARS → Y-VARS → 1:Function.
Press TRACE (F1) on the graph, then type the x-value and EXE. Or use the Table view (MENU → Table) to see multiple values.
On the graph, press TRACE and type the x-value, then ENTER. Or on a Calculator page type f1(3) to evaluate the stored function at x = 3.
On a TI-84 Plus CE
After graphing the function, you can evaluate it at any x-value.
Method 1 - Table: 2nd → GRAPH (TABLE), scroll to the x you want. Method 2 - Trace: press TRACE, then type the x-value and press ENTER. Method 3 - Home screen: type Y1(value) e.g. Y1(3) using VARS → Y-VARS → 1:Function.
For models: substitute the x-value into the regression equation stored in the calculator (see 'Use a fitted model to make predictions').
Tip: Trace gives an approximate value by cursor position - typing the x-value after pressing TRACE gives the exact value.
On a Casio fx-CG50 and fx-CG100
After graphing the function, you can evaluate it at any x-value.
Press TRACE (F1) on the graph, then type the x-value and EXE. Or use the Table view (MENU → Table) to see multiple values.
For models: substitute the x-value into the regression equation stored in the calculator (see 'Use a fitted model to make predictions').
Tip: Trace gives an approximate value by cursor position - typing the x-value after pressing TRACE gives the exact value.
On a TI-Nspire CX
After graphing the function, you can evaluate it at any x-value.
On the graph, press TRACE and type the x-value, then ENTER. Or on a Calculator page type f1(3) to evaluate the stored function at x = 3.
For models: substitute the x-value into the regression equation stored in the calculator (see 'Use a fitted model to make predictions').
Tip: Trace gives an approximate value by cursor position - typing the x-value after pressing TRACE gives the exact value.
Here's a real IB-style question that uses exactly this technique.
EasyCalculatorPaper 2[2 marks]
For f(x) = x² − 4x + 3, find f(5).
8
Mark it
Correct2 / 2 marks
Worked solution & mark scheme:
M1 Substitute x = 5 into f(x)
A1 8
Common questions
When would I need to evaluate a function at a point in IB Maths?
Read off the exact y-value for a given x - useful for checking answers and for questions that ask for a specific coordinate. A question asks for f(a) for a specific value of a, rather than the general expression. Checking a coordinate on a graph without reading it off by eye.
How do I evaluate a function at a point on a TI-84 Plus CE?
1. After graphing the function, you can evaluate it at any x-value. 2. Method 1 - Table: 2nd → GRAPH (TABLE), scroll to the x you want. Method 2 - Trace: press TRACE, then type the x-value and press ENTER. Method 3 - Home screen: type Y1(value) e.g. Y1(3) using VARS → Y-VARS → 1:Function. 3. For models: substitute the x-value into the regression equation stored in the calculator (see 'Use a fitted model to make predictions').
How do I evaluate a function at a point on a Casio fx-CG50 and fx-CG100?
1. After graphing the function, you can evaluate it at any x-value. 2. Press TRACE (F1) on the graph, then type the x-value and EXE. Or use the Table view (MENU → Table) to see multiple values. 3. For models: substitute the x-value into the regression equation stored in the calculator (see 'Use a fitted model to make predictions').
How do I evaluate a function at a point on a TI-Nspire CX?
1. After graphing the function, you can evaluate it at any x-value. 2. On the graph, press TRACE and type the x-value, then ENTER. Or on a Calculator page type f1(3) to evaluate the stored function at x = 3. 3. For models: substitute the x-value into the regression equation stored in the calculator (see 'Use a fitted model to make predictions').
What should I watch out for when I evaluate a function at a point?
Trace gives an approximate value by cursor position - typing the x-value after pressing TRACE gives the exact value.
How are marks awarded when I evaluate a function at a point in an IB exam?
In the worked example on this page (2 marks, Paper 2), the marks are: M1: Substitute x = 5 into f(x); A1: 8.
