RECIPRoCOLS - alevel maths

Question 1

Describe the following transformations

y = f(x) +a

Answer 1

translate up by a

Question 2

y = f(x+a)

Answer 2

Translate left by a

Question 3

y = f(x)*a

Answer 3

multiply y-values by a

Question 4

y = f(x*a)

Answer 4

multiply multiply x-values by 1/a

Question 5

y = - f(x)

Answer 5

reflect in x axis

y’s become opposite sign

Question 6

y = f(-x)

Answer 6

Reflect in y axis

x’s become opposite sign

Question 7

y = |f(x)|

Answer 7

reflect any bits of the graph below the x-axis in the x-axis.

Question 8

y = f(|x|)

Answer 8

reflect the rhs of the graph in the y-axis (delete whatever was in the lhs)

Question 9

how will translations affect reciprocals?

Answer 9

they shift the asymptotes, and thus the whole graph

Question 10

how will squash/stretch change a reciprocal?

Answer 10

the line shape will change, the curves of the lines getting further from or closer to the origin.

Question 11

What are the three key steps for drawing any transformations to reciprocal graphs?

Answer 11

1. consider the simple recipricol y=1/x
2. Think of how the two ASYMPTOTES at x=0 anf y=0 of the simple reciprocal change (this will happen in translations)
3. Think if the line shape changes (this happens in squash/stretch)

(note that in squash & stretching the asympotes dont change, the line shape does