Variation of Parameters in Functions — Australian Curriculum (ACARA) Grade 9 Mathematics Worksheet

Australian Curriculum (ACARA)

Grade 9

Mathematics

40 questions

Experimenting with the effects of variation of parameters on graphs of related functions using digital tools, making connections between graphical and algebraic representations (ACARA AC9M9A06), from a parameter-exploration angle.

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Variation of Parameters in Functions

This worksheet explores the effects of varying parameters on the graphs of linear, quadratic, hyperbolic, and circular functions and relations, making connections between graphical and algebraic representations. Total: 40 marks.

Section A: Linear Functions

Analyse the effects of parameters on linear functions of the form y = mx + c.

In the equation y = mx + c, what is the effect of increasing the value of c?

The graph shifts vertically upwards The graph shifts horizontally to the right The graph becomes steeper The graph becomes less steep

How does changing the value of m from 2 to 4 in y = mx + c affect the graph?

The line becomes steeper The line becomes less steep The line shifts up The line reflects in the x-axis

If the graph of y = 2x + 1 is shifted down by 3 units, what is the new equation?

y = 2x + 4 y = 2x - 2 y = -x + 1 y = 2(x-3) + 1

What does a negative value for the parameter m indicate?

The line is horizontal The line slopes upwards from left to right The line slopes downwards from left to right The line passes through the origin

In the equation y = mx + c, the parameter c represents the ________.

Section B: Quadratic Functions

Analyse the effects of parameters on quadratic functions of the form y = a(x-h)^2 + k.

Section C: Hyperbolic Functions

Analyse the effects of parameters on hyperbolic functions of the form y = \frac{a}{x-h} + k.

Section D: Circles

Analyse the effects of parameters on the equation of a circle: (x-h)^2 + (y-k)^2 = r^2.

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