Graphing and Polynomials

Recognising the equation of a semi-circle centred at the origin. Top, bottom, left and right.

Recognising the equation of a circle.

Recognising that $(x-a)^2+(y-b)^2=r^2$ is a circle of radius $r$ with centre $(a,b)$ 

Completing the square twice to determine the radius and centre of a circle.

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Identifying y=mx+b given two points

Given one point and the gradient determine the equation of the line.

Given the graph of the line determine the equation of the line.

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Identifying gradient and $y$-intercept from $y=mx+b$.

Graphing $y=ab^{\pm x+d}+c$

Graphing $y=ab^x+c$

Graphing exponentials with a base between 0 and 1 and no transformations take place.

The easiest type of exponential to graph where the base is greater than 1 and no transformations take place.

Identifying some of the basic properties (intercepts, asymptotes, quadrants) of a rational function (quadratic over linear)

The easiest type of exponential to graph where the base is greater than 1 and no transformations take place.

Graphing $y=a\log_{b}(x)+c$

Graphing $y=a\log_{b}(\pm x+d)+c$

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Understanding the general facts about polynomials of degree n.

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$y=mx+b$

Horizontal and vertical shifts and scales of a random cubic spline

of a random cubic spline

of a random cubic spline

Horizontal and vertical shifts and scales of a random cubic spline

Horizontal and vertical shifts and scales of a random cubic spline