Functions

Question 1

y = -f(-x)

what would the co-ordinates of the point (x,y) look like when this function is applied to it?

Answer 1

(-x, -y) – reflection in the origin / half turn

Question 2

y = -f(x)

what would the co-ordinates of the point (x,y) look like when this function is applied to it?

Answer 2

(x, -y) – reflect in the x-axis

Question 3

y = af(cx + d) + b

what would the co-ordinates of the point (x,y) look like when this function is applied to it?

Answer 3

([x - d]/c, ay + b) –

• translate (move) in the x-direction
• stretch or squash in the x-direction – depends on if the value of c is > 1
• stretch or squash in y-direction
• then translate in the y-direction

Question 4

y = af(x)

what would the co-ordinates of the point (x,y) look like when this function is applied to it?

Answer 4

(x,ay) – a stretch or squash in the y-direction depending on whether the value of a > 1 or < 1

Question 5

y = af(x) + b

what would the co-ordinates of the point (x,y) look like when this function is applied to it?

Answer 5

(x, ay + b) – stretch/squash then translation in the y direction

Question 6

y = f(-x)

what would the co-ordinates of the point (x,y) look like when this function is applied to it?

Answer 6

(-x, y) – reflect in the y-axis

Question 7

y = f(cx + d)

what would the co-ordinates of the point (x,y) look like when this function is applied to it?

Answer 7

([x - d]/c, y) – translate then stretch/squash in the x direction

Question 8

y = f(cx)

what would the co-ordinates of the point (x,y) look like when this function is applied to it?

Answer 8

(x/c, y) – stretch/squash in the x-direction

Question 9

y = f(x + d)

what would the co-ordinates of the point (x,y) look like when this function is applied to it?

Answer 9

(x - d, y) – translate (move) in the x-direction

so when d is negative what direction does the graph move in? Careful!

Question 10

y = f(x)

Answer 10

(x,y)

Question 11

y = f(x) + b

what would the co-ordinates of the point (x,y) look like when this function is applied to it?

Answer 11

(x, y + b) – a translation (move) in the y-direction

Question 12

function

Answer 12

a rule that relates each member of a set to exactly one member of another