Part A:
The plot for the function f(x) and g(x) is attached. The purple curve represents f(x) and the black line represents g(x).
Part B:
The graph of f(x) shows that f(x) is an exponential function.
The graph of g(x) shows that g(x) is a linear function.
Part C:
As x increases from left to right, the function f(x) increases very rapidly.
As x increases from left to right, the function f(x) increases at a constant rate.
Part D:
From the graph it can be seen than the valus of x for which the values of the function are equal are: x = -4 and x = 1.19.
Answer:17
Step-by-step explanation:
Lin's hourly rate is 15 dollars per hour.
The x represents the change that occurs per hour the 500 is the performance bonus which is a set constant amount.
Given: f(x) = x³ - 4x² + 2
Note that
f(x+h) - f(x) = (x+h)³ - 4(x+h)² + 2 - (x³ - 4x² + 2)
= x³ + 3x²h + 3xh² + h³ - 4(x² + 2xh + h²) + 2 - x³ + 4x² - 2
= 3x²h + 3xh² + h³ - 8xh - 4h²
Therefore
[f(x+h) - f(x)]/h = 3x² +3xh + h² - 8x - 4h
That is
f'(x) = 3x² - 8x
f'(3) = 3(3²) - 8(3) = 3
Answer: 3
The unit rate would probably be 21 per 3.5