Functions and Graphs - Short Problems

A snail slithers around on a coordinate grid. At what position does he finish?

Lisa's bucket weighs 21 kg when full of water. After she pours out half the water it weighs 12 kg. What is the weight of the empty bucket?

Which of these graphs could be the graph showing the circumference of a circle in terms of its diameter?

How could you use this graph to work out the weight of a single sheet of paper?

Can you draw the graph of $y=x$ after it has been rotated $90$ degrees clockwise about $(1,1)$?

Find the point on the line segment AB that is twice as far from B as it is from A.

Find the area of the triangle enclosed by these lines.

How many lattice points are there in the first quadrant that lie on the line 3x + 4y = 59 ?

Can you find the area between this graph and the x-axis, between x=3 and x=7?

What is the area of the triangle formed by these three lines?

How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?

The curve $y=x^2-6x+11$ is rotated through $180^\circ$ about the origin. What is the equation of the new curve?

Sketch the graph of the curve $y^2 = x(2-x)$

A triangle of area 64 square units is drawn inside the parabola $y=k^2-x^2$. Find the value of $k$.

Can you find the gradients of the lines that form a triangle?

Use the information about the triangles on this graph to find the coordinates of the point where they touch.

Which of these lines comes closer to the origin?