Understanding the shape of a parabola, cubic curve, and reciprocal graph and then applying key features like positive/negative coefficients and $$y$$-intercepts enables pupils to infer much about the equation without needing actual coordinate values.

Keywords

Quadratic - A quadratic is an equation, graph, or sequence whereby the highest exponent of the variable is 2
Cubic - A cubic is an equation, graph, or sequence whereby the highest exponent of the variable is 3
Exponential - The general form for an exponential equation is y = ab^x where a is the coefficient, b is the base and x is the exponent.
Asymptote - An asymptote is a line that a curve approaches but never touches.

Ask pupils to verbalise their reasoning when matching graphs to equations. "How do you 'know' that is the graph of... ?" is a key question to ask once pupils have matched a pair. Being able to justify with technical vocabulary is a powerful skill in mathematics.

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This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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6 Questions

Q1.

__________ is a line that a curve approaches but never touches.

A tangent

A linear graph

Correct answer: An asymptote

An axis

Q2.

Laura plots the graph of $$y=x^3$$. When the $$x$$ coordinate is $$-4$$, the $$y$$ coordinate is .

Correct Answer: -64, y=-64

Q3.

Andeep plots the reciprocal graph $$y={1\over{x}}$$. Which of these will be coordinate pairs?

Correct answer: $$(3,{1\over3})$$

$$(0,0)$$

$$(-2,2)$$

$$(-2,-2)$$

Correct answer: $$({1\over4},4)$$

Q4.

Jun graphs the circle $$x^2+y^2=16$$. When the $$y$$ coordinate is $$3$$, the $$x$$ coordinate is .

$$5$$

$$4$$

Correct answer: $$\sqrt7$$

Correct answer: $$-\sqrt7$$

$$5$$

Q5.

The general form of the equation of a circle with centre origin is $$x^2+y^2=r^2$$. What is the radius of the circle graphed by the equation $$x^2+y^2=25$$?

$$25$$

$$25^2$$

Correct answer: $$5$$

$$-5$$

Q6.

A quarter circle with radius 7 overlaps a square of length 7. Which of these calculations will give the shaded area?

Correct answer: $$7^2-{{1\over{4}}\times{\pi}\times7^2}$$

$$7^2-{{1\over{4}}\times{\pi}\times14}$$

$$49-49{\pi}$$

$$7^2-{{1\over{4}}\times{\pi}\times14^2}$$

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6 Questions

Q1.

This is an example of __________ graph.

a cubic

an exponential

a quadratic

Correct answer: a reciprocal

Q2.

This is an example of __________ graph.

a cubic

Correct answer: an exponential

a quadratic

a reciprocal

Q3.

How can you tell that this is not the graph of $$y={5\over{x}}$$?

It is not a reciprocal graph.

$$y={5\over{x}}$$ would not have the axes as asymptotes.

Correct answer: For $$y={5\over{x}}$$ when $$x$$ is positive $$y$$ would be positive.

Correct answer: For $$y={5\over{x}}$$ when $$x$$ is negative $$y$$ would be negative.

This might be the graph $$y={5\over{x}}$$

Q4.

Which of these could be the equation of this graph?

$$y=x^3-3$$

$$y={-3\over{x}}$$

$$y=3-x^3$$

$$y={-3\over{x}}-3$$

Correct answer: $$y=-x^3-3$$

Q5.

Which of these could be the equation of this graph?

Correct answer: $$y={4\over{x}}-2$$

$$y=2-{4\over{x}}$$

$$y=2-4^x$$

$$y=-4-2^x$$

$$y={4\over{x}}$$

Q6.

The circle $$x^2+y^2=49$$ and the line $$x+y=0$$ are drawn on the same axes. What is the area of the region bound by the circumference of the circle, the line $$x+y=0$$, and the $$y$$ axis?

$$\pi\times7^2$$

$${1\over2}\times\pi\times7^2$$

$${1\over4}\times\pi\times49^2$$

$${1\over4}\times\pi\times7^2$$

Correct answer: $${1\over8}\times\pi\times7^2$$