M - Pure 1 - 4) Graphs and transformations

Question 1

Locations of the asymptotes on the graphs of y = k/x and y = k/x²

Answer 1

x = 0 and y = 0

Question 2

Quadrants used on the graphs of y = +k/x | y = -k/x | y = +k/x² | y = -k/x²

Answer 2

• y = +k/x → TR and BL
• y = -k/x → TL and BR
• y = +k/x² → TL and TR
• y = -k/x² → BL and BR

Question 3

Method to find the coordinates of the point of intersection of two functions on a graph?

Answer 3

1. Find the solution to f(x) = g(x) to find x-ordinate
2. Substitute that into f(x) to find y-ordinate

Question 4

List of graph transformations and their effects

Answer 4

• y = f(x + a) → (^-a₀)
• y = f(x) + a → (⁰_a)
• y = f(ax) → Stretch by scale factor 1/a horizontally
• y = af(x) → Stretch by scale factor a vertically
• y = -f(x) → Reflection in the x-axis
• y = f(-x) → Reflection in the y-axis

Question 5

Something else translated when a function is translated

Answer 5

Any asymptotes