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 with a modulus, from $f(x)=nx-m|x|$ to $f(ax)$.

Finding the transformation of an exponential function $f(x)=e^{nx}$ to $f(ax)$.

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

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

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

Finding the transformation of a function with a modulus, from $f(x)=nx-m|x|$ to $f(x+a)$.

Finding the transformation of an exponential function $f(x)=e^{nx}$ to $f(x+a)$.

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 $f(ax+b)$.

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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.