Chapter 4 Graphs and Transformations

Question 1

What does a cubic function have the form of?

Answer 1

F(x) = ax^3 + bx^2 + cx + d where a is non zero

Question 2

How do you find the point where a graph crosses the x-axis?

Answer 2

If p is the root of the function f(x), then the graph of y = f(x) touches/crosses the x axis at the point(s) (p,0)

Question 3

What does a quartic function have the form of?

Answer 3

F(x) = ax^4 + bx^3 + cx^2 + dx + e where a, b, c, d, and e are real numbers and a is non-zero

Question 4

How do you sketch graphs of reciprocal functions?

Answer 4

By considering their asymptotes

Question 5

Where do the graphs of y=k/x and y=k/x^2 gave asymptotes?

Answer 5

At x = 0 and y = 0

Question 6

How do you find the x-coordinates of the points of intersection of the curves y = f(x) and y = g(x)?

Answer 6

The x-coordinates at the point of intersection of the curves with equations y = f(x) and y = g(x) are the solutions to the equation f(x) = g(x)

Question 7

What transformation is the graph of y = f(x) + a?

Answer 7

A translation of the graph y = f(x) by the vector 0/a (0 up/down and a left/right)

Question 8

What transformation is the graph of y = f(x + a)?

Answer 8

A translation of the graph y = f(x) by the vector -a/0 (-a up/down and 0 left/right)

Question 9

What happens to asymptotes when you translate a function?

Answer 9

Any asymptotes are also translated

Question 10

What transformation is the graph of y = af(x)?

Answer 10

A stretch of the graph y = f(x) by a scale factor of a in the vertical direction

Question 11

What transformation is the graph of y = f(ax)?

Answer 11

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

Question 12

What transformation is the graph of y = -f(x)?

Answer 12

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

Question 13

What transformation is the graph of y = f(-x)?

Answer 13

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