Functions and graphs (Maths Methods Units 3 and 4) quiz

All real $x$

$x > 3$

$x \ge 3$

$x \le 3$

$\frac{x - 5}{2}$

$2x + 5$

$5 - 2x$

$\frac{x + 5}{2}$

$(2, 3)$

$(-2, 3)$

$(2, -3)$

$(3, 2)$

A horizontal asymptote at $y = 4$ and a vertical asymptote at $x = 0$

A vertical asymptote at $x = 4$ and horizontal asymptote $y = 0$

An $x$-intercept at $4$, where the curve crosses the horizontal axis

A vertex at $(4, 0)$, the turning point of the parabola

$\log_2(6)$

$3$

$2$

Cannot be simplified

$3$

$4$

$8$

$27$

$2\pi$

$\frac{\pi}{2}$

$4\pi$

$\pi$

$[-1, 3]$

$[-1, 1]$

$[0, 2]$

$[-2, 2]$

$x^2 + 3$

$x(x + 3)$

$(x + 3)^2$

$x^2 + x + 3$

$p(x)$ must be a constant function everywhere

$p(x)$ has no other zeros apart from $x = 2$

$p$ must have degree exactly equal to $1$

$x - 2$ is a factor of $p(x)$

Reflection in the $x$-axis, translate left $3$, translate up $4$

Translate right $3$ units, then translate up $4$ units, then reflect in the $y$-axis

Reflect in the $y$-axis, then translate up $4$ units

Reflect in the $x$-axis only, with no translations applied

I will sketch the graph straight away by plotting a handful of points from a table of values and joining them up freehand, since a curve through enough points will always show every feature I need to mark.

Identify the parent function and list the transformations in order: reflection, dilation, translation. Then mark key features (intercepts, asymptotes, stationary points) before sketching.

Functions are mappings, so I will simply describe in words what the rule does to each input value.

Graphs are visual, so a neat picture on its own should be enough to earn the available marks.