Finding the transformation of a function $f(x)=\frac{nx^2}{x+c}$ to $f(x+a)$.

Finding the transformation of a quadratic function $f(x)=ax^2+bx+c$ to $f(x+n)$.

Finding the transformation of a linear function $f(x)=mx+c$ to $f(x+a)$.

Finding the transformation of a function of the form $f(x)=\frac{mx+c}{x^2-d}$ to $f(ax)+b$.

Finding the transformation of a function of the form $f(x)=\frac{mx+c}{x^2-d}$ to $af(bx)$.

Finding the transformation of a function of the form $f(x)=\frac{mx+c}{x^2-d}$ to $af(x+b)$.

Finding the transformation of a function of the form $f(x)=\frac{mx+c}{x^2-d}$ to $f(ax+b)$.

Finding the transformation of a linear function $f(x)=mx+c$ to $f(ax)+b$.

Finding the transformation of a linear function $f(x)=mx+c$ to $af(bx)$.

Finding the transformation of a linear function $f(x)=mx+c$ to $af(x+b)$.

Finding the transformation of a linear function $f(x)=mx+c$ to $f(ax+b)$.

An explore mode activity containing a lot of questions, for students to check their understanding of the information in the "Getting Started" material.

Note: This question was written for students accessing Numbas exams through the Numbas LTI tool. Some of the information does not apply to exams accessed standalone or through a generic SCORM player.

This question gives information for students on how to answer number entry parts, with some opportunities to try submitting answers.

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Student finds a basis for kernel and image of a matrix transformation. Any basis can be entered; there is a custom marking algorithm which checks if it is a correct basis.

There are options to adjust this question fairly easily, for example to get different variants for practice and for a test, by changing the options in the "pivot columns" in the variables. You should be careful to think about and test your pivot options, as some are easier or harder than others, and some don't work very well.

sin horizontal shifted Working 1_11_16

This uses an embedded Geogebra graph of a sine curve $y=a\sin (bx+c)+d$  with random coefficients set by NUMBAS.

The easiest type of exponential to graph where the base is greater than 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.

Just what the title says, I guess. I couldn't find a 0^0 that didn't converge to 1 except things like x^(1/ln(x)) as x->0, but they just need the e^ln() transformation, not L'hopital's rule!

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This question relies on using information in the pie chart to find a ratio.

These questions focus on finding a ratio (or fraction) from the information given.

First compute matrix times vector for specific vectors. Then determine domain and codomain and general formula for the matrix transformation defined by the matrix.

First compute matrix times vector for specific vectors. Then determine domain and codomain and general formula for the matrix transformation defined by the matrix.

Randomising the number of rows in the matrix, m, makes the marking algorithm for part c) slightly complicated: it checks whether it should include the third gap or not depending on the variable m. For the correct distribution of marks, it is then necessary to do "you only get the marks if all gaps are correct". Otherwise the student would only get 2/3 marks when m=2, so the third gap doesn't appear.

First compute matrix times vector for specific vectors. Then determine domain and codomain and general formula for the matrix transformation defined by the matrix.

Randomising the number of rows in the matrix, m, makes the marking algorithm for part c) slightly complicated: it checks whether it should include the third gap or not depending on the variable m. For the correct distribution of marks, it is then necessary to do "you only get the marks if all gaps are correct". Otherwise the student would only get 2/3 marks when m=2, so the third gap doesn't appear.