Sketching curves

Question 1

What does the graph of y=ax³+bx²+cx+d look like for a>0?

Answer 1

As x tends to infinity, so does y, and as x tends to minus infinity so does y

Question 2

What does the graph of y=ax³+bx²+cx+d look like for a<0?

Answer 2

As x tends to infinity, y tends to minus infinity, and vice versa

Question 3

What is an asymptote?

Answer 3

A line which a curve gets infinitely close to without ever reaching

Question 4

What does the graph of y=c/x look like for c>0?

Answer 4

The top right and bottom left quadrants have a curve with asymptotes x=0 and y=0

Question 5

What does the graph of y=c/x look like for c<0?

Answer 5

The top left and bottom right quadrants have a curve with asymptotes x=0 and y=0

Question 6

What effect does the magnitude of a constant c have in the graph of y=c/x?

Answer 6

The greater c is, the further away a given x value’s point is from the origin

Question 7

What does the graph of y=f(x+a) where a is a constant look like, compared to the graph of y=f(x)?

Answer 7

It has been horizontally translated by -a

Question 8

What does the graph of y=f(x)+a where a is a constant look like, compared to the graph of y=f(x)?

Answer 8

It has been vertically translated by a

Question 9

What does the graph of y=f(ax) where a is a constant look like, compared to the graph of y=f(x)?

Answer 9

It has been horizontally stretched by a scale factor of 1/a

Question 10

What does the graph of y=af(x) where a is a constant look like, compared to the graph of y=f(x)?

Answer 10

It has been vertically stretched by a scale factor of a