Pure- Graphs and transformations (4)

Question 1

What is the form of a cubic equation?

Answer 1

f(x)=ax^3 + bx^2 + cx + d

where a,b,c,d are real numbers and a isn’t 0

Question 2

What happens if p is the root of f(x)?

Answer 2

y=f(x) touches or crosses the x-axis at (p,0)

Question 3

What is the form a quartic equation?

Answer 3

f(x)=ax^4 + bx^3 +cx^2 + dx + e

Question 4

What are the asymptotes of y=k/x and y=k/x^2 where k is a real constant?

Answer 4

x=0

y=0

Question 5

What is an asymptote?

Answer 5

A line which the graph approaches but never reaches.

Question 6

What are the x-coordinates to the intersections of y=f(x) and y=g(x)?

Answer 6

The solutions to f(x)=g(x)

Question 7

What transformation does y=f(x)+a correspond to ?

Answer 7

A translation of y=f(x) by a units vertically

Question 8

What transformation does y=f(x+10) correspond to?

Answer 8

A translation of y=f(x) by -a units horizontally

Question 9

What does the transformation y=af(x) correspond to?

Answer 9

A vertical stretch of y=f(x) by scale factor a

Question 10

What does the transformation y=f(ax) correspond to?

Answer 10

A horizontal stretch of y=f(x) by scale factor 1/a

Question 11

What does the transformation y=-f(x) correspond to?

Answer 11

A reflection of y=f(x) in the x-axis

Question 12

What does the transformation y=f(-x) correspond to?

Answer 12

A reflection of y=f(x) in the y-axis