Functions/ Transformations

Question 1

y=f(x) +c

Answer 1

Vertical Shift upwards
Raise the graph of f(x) by c units
add c to your coordinates

Question 2

y = f(x) - c

Answer 2

Vertical Shift downwards
lower the graph of f(x) by c units
subtract c from y coordinate

Question 3

y = f(x +c)

Answer 3

Horizontal shift left
Shift the graph f(x) to the left c units
subtract c from x coordinate

Question 4

y = f(x-c)

Answer 4

Horizontal shift to the right
Shift graph f(x) to the right c units
add c to x coordinate

Question 5

y=-f(x)

Answer 5

Reflection about the x axis
Reflect the graph f(x) to the right c units
- multiply each y coordinate by -1

Question 6

y= f(-x)

Answer 6

reflection about the y axis
reflect the graph f(x) about the y axis
multiply each x coordinate by -1

Question 7

y = cf(x), c>1

Answer 7

Vertically stretching the graph of f (x) (c>1)
multiply each y coordinate by c

Question 8

y= cf(x), 0<c<1

Answer 8

Vertically compressing the graph f f (x) (0<c<1)
multiply each y coordinate by c

Question 9

y = f (cx),c>1

Answer 9

Horizontally compressing the graph f f(x) (c>1)

Question 10

y= f(cx), 0<c<1

Answer 10

Horizontally stretching the graph of f(x) (0<c<1)
divide each x coordinate by c

Question 11

y=1/f(x)

Answer 11

take the reciprocal of each y coordinate of f(x)

Question 12

how do i find the range

Answer 12

make x the subject

Question 13

how do i find a range of a function (fraction)