Graphs And Transformations

Question 1

What form does a cubic function have?

Answer 1

f(x) = ax³ + bx² + cx + d

Where a, b, c, d are real numbers and a doesnt equal 0.

Question 2

How do you sketch cubic functions?

Answer 2

1. Identify orientation-
   Positive (quadrants 3 to 1)
   Negative (quadrants 2 to 4)
2. Label roots
3. Label y intercept

Question 3

What form does a quartic function have?

Answer 3

f(x) = ax⁴ + bx³ + cx² + dx + e

Where a, b, c, d, e are real numbers and a doesnt equal 0.

Question 4

How do you sketch quartic functions?

Answer 4

1. Identify orientation-
   Positive (quadrants 2 to 1)
   Negative (quadrants 3 to 4)
2. Label roots
3. Label y intercept

Question 5

What is an asymptote?

Answer 5

An asymptote is a line which a curve approaches but never reaches.

Question 6

Reciprocal Graphs?

Answer 6

y = k / x

y = k / x²

where k is a real constant, and the graphs have asymptotes at x = 0 and
y = 0.

Question 7

For a function of the form:

y = a / (x - h) + k

How do you find:
• The vertical asymptote
• The horizontal asymptote

Answer 7

Vertical asymptote (how to find it):
Set the denominator = 0.

x-h=0

Solve for x.
This gives the vertical asymptote x=h

Horizontal asymptote (how to find it):
Look at the constant added outside the fraction.

y=k