Horizontal and vertical shifts and scales 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

of a random cubic spline

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

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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.

Find the $x$ and $y$ intercepts of a circle.

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 some of the basic properties (intercepts, asymptotes, quadrants) of a right hyperbola.

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Understanding the general facts about polynomials of degree n.

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This question plots a general amplitude modulated carrier signal defined by $v_s(t) = (V_{DC} + V_m \cos(2\pi f_m t))\cos(2\pi f_c t)$, where $V_{DC}$ is a DC offset, $V_m$ is the message amplitude, $f_m$ is the message frequency and $f_c$ is the carrier frequency ($f_c = 20f_m$ in this question). The student must identify the values of $V_{DC}$ and $V_m$ and enter these values into the appropriate gaps in the equation of the AM signal.

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Compute a table of values for a quadratic function. A JSXgraph (the graph paper) plot shows the curve going through the entered values.