Chapter 4: Graphs And Transformations

Question 1

When there is a cubic graph, with the 3 roots having the x values: 0, positive and negative, how do you determine whether the line will start from above or below the x axis?

Answer 1

If coefficient of x^3 is negative, it will start from above.

If positive, it will start from below.

Question 2

What is the most simple equation that a reciprocal graph has and what does it always feature?

Answer 2

Y=k/x.

An asymptote that is always a line on the axis.

Question 3

Define an asymptote:

Answer 3

An imaginary vertical or horizontal line which the graph approaches but never reaches.

Question 4

What does y=k/x look like on a graph?

Answer 4

2 L shapes in the first and third quadrant (this one is rotated 180°)

Question 5

What does y=-k/x look like on a graph?

Answer 5

2 L shapes in the second (this one is rotated 90° clockwise) and fourth quadrant (this one is rotated 90° anti-clockwise).

Question 6

What does y=k/x² look like on a graph?

Answer 6

2 L shapes in the first and fourth quadrant (this one is rotated 90° anti-clockwise).

Question 7

What does y=-k/x² look like on a graph?

Answer 7

2 L shapes in the second (this one is rotated 90° clockwise) and third quadrant (this one is rotated 180°).

Question 8

As ‘k’ from y=k/x gets larger (all other things equal), what happens to the graph?

Answer 8

Y=k/x moves further away from asymptote.

Question 9

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

Answer 9

It translates it by VECTOR (0, a).

Question 10

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

Answer 10

It translates it by VECTOR (-a, 0).

Question 11

What does y= af(x) do to y=f(x) (a is positive)?

Answer 11

It stretches the graph in the y-direction by scale factor ‘a’.
All y-coordinates are multiplied by ‘a’.