Functions and Graphs Questions and Answers

The diagram shows the graph of $y = f(x)$, passing through $A(-1, 0)$, $B(0, 1)$ and $C(1, 0)$. On the graph of $y = f(-x) + 3$, the image of $B$ is

Find the set of values of $x$ which satisfy $|3x + 2| < -x + 1$.

Given that $-4 < x < 2$ is the solution of the inequality $|x + a| < b$, find the values of $a$ and $b$.

Find the inverse of $f(x) = ax + b$, where $a \ne 0$ and $b$ are constants.

Solve the inequality $|x-1| < x$.

Solve the inequality $|x^2-2|<-x$.

In solving $|x^2-2|<-x$ by cases, why is only $x=-2$ (not $x=1$) accepted from the case $x^2-2\ge0$, and only $x=-1$ (not $x=2$) accepted from the case $x^2-2<0$?

The graph $y=f(x)$ has $y$-intercept $(0,16)$. State the $y$-intercept of $y=f(x)-6$.

The graph $y=f(x)$ has $x$-intercepts $(-2,0)$, $(2,0)$ and $(4,0)$. State the $x$-intercepts of $y=f(x+1)$.

The graph $y=f(x)$ has $y$-intercept $(0,16)$. State the $y$-intercept of $y=-\tfrac12f(x)$.

The graph $y=f(x)$ has $x$-intercepts $(-2,0)$, $(2,0)$ and $(4,0)$. State the $x$-intercepts of $y=f(2x)$.

The function $f:x\mapsto\dfrac{m}{x}+n$. State the domain of $f(x)$.

The function $f:x\mapsto\dfrac{m}{x}+n$ satisfies $f(-1)=1\tfrac12$ and $f(2)=9$. Find the values of $m$ and $n$.

Given $f(x)=\dfrac5x+\dfrac{13}2$, find an expression for $f^{-1}(x)$.

Given $f^{-1}(x)=\dfrac{10}{2x-13}$, evaluate $f^{-1}(4)$.

Solve the inequality $\dfrac2{x-3}<\dfrac3{x-4}$.

The point $(1,5)$ satisfies the simultaneous equations $n^2x+my=14$ and $ny-mx=8$. Find one valid pair of values for $n$ and $m$.