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

This question uses a Geogebra applet to solve a linear program with two variables using the graphical method. It contains three steps:

1. Construct the feasible area (polygon) by adding the constraints one by one. The students can see what happens when the constraints are added.
2. Add the objective function, and the level set of the objective value is shown, as well as its (normalised) gradient.
3. Compute the optimal solution by moving the level set of the objective around.

Drag points on a graph to the given Cartesian coordinates. There are points in each of the four quadrants and on each axis.

Find the equation of the line that passes through given points

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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.

Compute a table of values for a quadratic function. A JSXgraph (the graph paper) plot shows the curve going through the entered values. The student input is now disconnected from the graph so that they slide the points usually after they input the values and the answer fields are not updated.

This question allows you to practice identifying the coordinates of points on graphs.

This question allows you to practice identifying the coordinates of points on graphs.

A random graph is drawn and students are asked whether it represents a function or not.

A random graph is drawn and students are asked whether it represents a function or not.

Students are supposed to use Excel (or similar) to find the answers (e.g., enter coordinates of two points then plot and add trendline).

Uses an embedded Geogebra graph of a line $y=mx+c$ with random coefficients set by NUMBAS.

This uses an embedded Geogebra graph of a line $y=mx+c$ with random coefficients set by NUMBAS.

For the graphs in HELM Book 2 Figure 30, identify which are one-to-one, and which are many-to-one.

The student is shown one graph, and asked to type the adjacency matrix

Alternative version of Graphs: Match graph to its adjacency matrix, where the student must match an adjacency matrix to a graph.

Practicing skills required for sketching line graphs depicting the temperature of a mixture according to time. The question includes: a) choosing the accurate sketch from a list, and b) identifying the initial temperature of the mixture. 

Practicing skills required for sketching line graphs depicting DNA melting temperature according to the percentage of GC content. The question includes: a) identifying the  vertical intercept, b) choosing the accurate sketch from a list, and c) interpreting elements of the sketch in context. 

Interpreting line graphs depicting the melting temperature of DNA depending on the percentage of GC content. Estimating the melting temperature given a GC percentage and vice versa.

The question includes a quadratic graph depicting the relationship between the frequency of an allele A at a genetic locus in a diploid population and the fitness of a population with this frequency of allele A. The aim is to estimate the maximum and minimum fitness of the population and the corresponding frequency of allele A.

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This question gives the student the formula for the charge on a capacitor as a function of time then asks them to find the value of k, the exponential constant given other values and hence write out the formula for the given case. A custom function (in Extensions & scripts) extracts the student's formula and plots it on a JSXGraph object in the question. The student is then asked to evaluate the function at a given point using the plot or other methods. The value of the capacitor (Q_0), time (t) and charge at time t are randomised as is the value at which the formula is to be evaluated.

Draw the annulus given by a double inequality. The user moves circles on an interactive jsxgraph.

Given a graph of a circle, write down its equation.

This uses an embedded Geogebra graph of a polar function with random coefficients set by NUMBAS.

Identify whether a function is odd, even or neither from its graph. Part of HELM Book 2.4.3.

Given a piecewise function determine whether the limit exists at two points. Part of HELM Book 2.4.1.

Determine whether three graphs are functions or not. Part of HELM Book 2.3.