• Apr 4th 2007, 09:01 PM
juiicycouture

1. Solve the following equation:

(x+1)^2 - 3(x+1) = 0

2. What is the maximum possible number of turning points for each of the following functions?

a) linear function
c) cubic function
d) quartic function

3. For the function f(x) = (x-4)(x+1)(x-1)
a) find the domain and range
b) find the real zeros, to the nearest tenth necessary
c) the y-intercepts
d) the end behaviour (what is this?)
e) any symmetry
f) the number of turning points
• Apr 4th 2007, 10:43 PM
earboth
Quote:

Originally Posted by juiicycouture
...
1. Solve the following equation:

(x+1)^2 - 3(x+1) = 0

Factor the term:
(x+1)^2 - 3(x+1) = (x+1)((x+1) - 3) = (x+1)(x-2) = 0

Therefore the solutions are: x = -1 or x = 2

Quote:

Originally Posted by juiicycouture
.
2. What is the maximum possible number of turning points for each of the following functions?

a) linear function
c) cubic function
d) quartic function

If n is the degree (or do you say grade?) of the function then the maximum number of turning points is n-1:
Code:

```prob  degree  max. number of turning points ------------------------------------------- a)        1                        0 b)        2                        1 (= vertex) c)        3                        2 d)        4                        3```
Quote:

Originally Posted by juiicycouture
3. For the function f(x) = (x-4)(x+1)(x-1)
a) find the domain and range
b) find the real zeros, to the nearest tenth necessary
c) the y-intercepts
d) the end behaviour (what is this?)
e) any symmetry
f) the number of turning points

a) There aren't any restrictions for x thus d = IR (the set of real numbers).
Because f has the degree 3 and the coefficient of x³ is 1 the values of the function reach from -∞ to +∞

b) f(x) = 0 if one of the factors is zero. Therefore the zeros are: x = -1, x = 1, x = 4

c) The y-intercept is f(0) = (-4)(1)(-1) = 4

d) If x --> -∞ then f(x) --> -∞
If x --> ∞ then f(x) --> ∞

e) Because f has the degree 3 there is only possible a point inflection. The centre of symmetry could only be the inflection point. With your function the graph of f is symmetric to the point ((4/3), -(56/27))

f) see #2: thus 2

EB
• Mar 25th 2009, 06:32 PM
TheMasterMind
Quote:

Originally Posted by juiicycouture

1. Solve the following equation:

(x+1)^2 - 3(x+1) = 0

2. What is the maximum possible number of turning points for each of the following functions?

a) linear function
c) cubic function
d) quartic function

3. For the function f(x) = (x-4)(x+1)(x-1)
a) find the domain and range
b) find the real zeros, to the nearest tenth necessary
c) the y-intercepts
d) the end behaviour (what is this?)
e) any symmetry
f) the number of turning points

i would approach these by graphing, the simplest way to figure them out. is this MHF4U work?

2.
a) no turning points, straight line
b) one turning point, a simple parabola
c) two turning points
d) three turning points