Year 10 Maths • AC9M10A05 • Authored homework
Investigating functions with digital tools
Experiment with functions and relations using digital tools, making and testing conjectures about how changing parameters affects graphs, tables and key features. Show working, use correct notation and check reasonableness.
Part A
Short-answer questions
What is a parameter in a function?
For y = mx + c, what does m control?
For y = mx + c, what does c control?
How does y = x^2 + 4 compare with y = x^2?
How does y = 2x^2 compare with y = x^2?
What can a graphing tool help you test quickly?
Why should conjectures from digital tools still be checked mathematically?
State one key feature you could compare between two graphs.
Correct this misconception: “If the graph looks right, the equation must be correct.”
Give one function family you could investigate with a graphing tool.
Part B
Long-answer questions
Use the family y = x^2 + k to make a conjecture about how k affects the graph.
Use the family y = a x^2 to describe how changing a affects graph width and direction.
Compare y = 2^x, y = 3^x and y = (1/2)^x using tables and graph descriptions.
Investigate y = mx + c for three values of m while c stays fixed. Describe the pattern.
A student changes two parameters at once and cannot explain the effect. Explain why one parameter should be changed at a time.
Design a digital-tool investigation into transformations of y = x^2, including a table of values to check one claim.
Use a graph to estimate a solution to x^2 = 2x + 3, then describe how to check algebraically.
Compare a table and a graph for identifying key features of a relation.
Create a conjecture about an exponential family y = a b^x and test it using three examples.
Write a full investigation report: question, function family, parameter tested, observations, conjecture and mathematical check.
Part C
Research and understanding task
Use or plan a graphing-tool investigation for one function family: linear, quadratic or exponential. Record the equations tested, describe the graph changes, make a conjecture and explain how you checked it.