How to cube function in range
Answers
Properties of Cubic Functions:
Cubic functions have the form
f (x) = a x3 + b x2 + c x + d
Where a, b, c and d are real numbers and a is not equal to 0.
The domain of this function is the set of all real numbers. The range of f is the set of all real numbers.
The y intercept of the graph of f is given by y = f(0) = d.
The x intercepts are found by solving the equation
a x3 + b x2 + c x + d = 0
The left hand side behaviour of the graph of the cubic function is as follows:
If the leading coefficient a is positive, as x increases f(x) increases and the graph of f is up and as x decreases indefinitely f(x) decreases and the graph of f is down.
If the leading coefficient is negative, as x increases f(x) decreases the graph of f is down and as x decreases indefinitely f(x) increases the graph of f is up.
Example 1
f is a cubic function given by
f (x) = x 3
a. Find the x and y intercepts of the graph of f.
b. Find the domain and range of f.
c. Sketch the graph of f.
Solution to Example 1:
• a - The y intercept is given by
(0 , f(0)) = (0 , 0)
• The x coordinates of the x intercepts are the solutions to
x3 = 0
• The x intercept are at the points (0 , 0).
• b - The domain of f (x) is the set of all real numbers.
• Since the leading coefficient (of x3) is positive, the graph of f is up on the right and down on the left and hence the range of f is the set of all real numbers.
Step-by-step explanation: