MASH Bath: Question Bank

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 $f(ax+b)$.

Finding the inverse of a function of the form $f(x)=\ln(ax)+b$ for $x>0$.

Finding the inverse of a function of the form $f(x)=e^{mx+c}$.

Finding the inverse of a function of the form $f(x)=\frac{x^2}{a}+b$ for $x \geq 0$.

Finding the inverse of a function of the form $f(x)=\frac{mx+c}{x+a},\,x\neq-a$.

Finding the inverse of a function of the form $f(x)=\frac{mx+c}{x},\,x\neq0$.

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

Evaluating a modulus function of the form $f(x)=ax+b|x|$ for a given value of $x$.

Evaluating a modulus function of the form $f(x)=x^2+m|x|$ for a given value of $x$.

Evaluating a modulus function of the form $f(x)=c-m|x|$ for a given value of $x$.

Evaluating a modulus function of the form $f(x)=m|x|+c$ for a given value of $x$.

Evaluating a cubic function for a given value of $x$.

Evaluating a quadratic function for a given value of $t$.

Evaluating a linear function for a given value of $x$.

Evaluating composite functions involving a linear function and a modulus function of the form $f(x)=|x|+c$, for a given value of $x$.

Determining the range of a function of the form $f = m|x| + a$.

Finding composite functions of a linear function and a modulus function.

Finding composite functions of a quadratic function and an exponential function.