Forest of Functions
A wandering elf’s path follows the spell y=2x+3y = 2x + 3y=2x+3. When the elf is 4 steps into the forest (x=4x = 4x=4), how far has she traveled?
y=11
A sorcerer multiplies two magical powers: x2 and x3. What is the combined spell power?
x5
A forest gnome counts 2x gold acorns and hides 5. If he ends up with 11 visible, how many did he have? 2x+5=11
x=3
A fairy’s wings form a triangle with base 10 m and height 8 m. What’s their shimmering area?
40 m2
A unicorn gallops 2.5 km across the meadow. How many meters did it travel?
2,500 m
A forest path’s slope is 3 and it passes through (2, 4). Write its equation.
y=3x−2
A potion labeled (x+2)2 is mixed. What’s the final formula after the explosion settles?
x2+4x+4
A mermaid collects coral shells: 3x−7=11. How many shells did she begin with?
x=6
A moonlit pond is perfectly round with a radius of 7 m. Find its circumference (pi--π=3.14).
43.96 m
A thunderbird flies 180 m in 12 seconds. What’s its speed through the storm?
15 m/s
A river spirit follows the current y=−2x+1y = -2x + 1y=−2x+1. Where does the spirit cross the water’s edge (the y-axis)?
(0,1)
A witch brews two potions: one of strength 3x2y and another of 2xy3. What’s their combined potency?
6x3y4
A rune stone glows according to x2−9x+20=0. What values of x make the magic stable?
x=4 or x=5
A wizard’s tower stands 10 m tall, 5 m wide, and 4 m deep. What’s its total volume of stone?
200 m3
A cauldron contains 3.5 L of glowing potion. How many milliliters is that?
3,500 mL
The paths of two fireflies cross: y=x+2y = x + 2y=x+2 and y=2x−1y = 2x - 1y=2x−1. Find their meeting point.
(3,5)
A cursed rune reads x2−9. Break its seal by factoring it completely.
(x−3)(x+3)
A fairy’s flight and a bat’s glide meet in the night sky: y=2x+1 and y=−x+4. Where do they meet?
(1,3)
A griffin’s flight forms a right triangle with legs 9 m and 12 m. Find the length of its soaring diagonal path.
15 m
A stone golem weighs 2.4 kg. Convert its weight to grams.
2,400 g
The glowing moonflower blooms according to f(x)=x2−4x+3f(x) = x2 - 4x + 3f(x)=x2−4x+3. Find the coordinates of its brightest bloom (the vertex).
(2,−1)
A dragon engraves (2x−3)(x+5) into a cave wall. Expand it to reveal its hidden message.
2x2+7x−15
The dragon’s fire follows x2−4x−12=0. Solve for x to find the moments of its flame’s peak.
x=6 or x=−2
The entrance to a crystal cave is a hexagon with perimeter 72 cm. How long is each sparkling side?
12 cm
A comet streaks 36 km across the night in 9 minutes. How fast is it flying in km/h?
240 km/h