Grade 12 Advanced Functions Worksheets

Solve each problem. Take your time.

1. 1.Evaluate log base 2 of 8. (log₂8)
2. 2.Using the power rule for logarithms, rewrite log(x^5) as a product.
3. 3.Find the average rate of change of the function f(x) = 3x² from x = 1 to x = 3.
4. 4.If f(x) = 2x + 1 and g(x) = x - 3, find f(g(x)).
5. 5.Expand log base 10 of (100 * y). (log₁₀(100y))
6. 6.Determine the vertical asymptote of the rational function f(x) = 5 / (x - 4).

Solve each problem. Show your work.

1. 1.Solve the logarithmic equation for x: log(x) + log(x - 3) = 1
2. 2.A company's profit P (in thousands of dollars) is modeled by the function P(x) = -x³ + 12x² - 36x, where x is the number of units sold (in thousands). Find the number of units sold that maximizes the profit.
3. 3.Consider the rational function f(x) = (x² - 4) / (x² - x - 6). Identify the vertical asymptotes, horizontal asymptote, and any holes in the graph of this function.
4. 4.A car travels 150 miles in 3 hours. What is its average speed? If the car's speed at any time t is given by v(t) = 3t² + 10t, find the instantaneous speed at t = 2 hours.
5. 5.A committee of 5 people is to be selected from a group of 8 men and 7 women. How many different committees can be formed if the committee must have exactly 3 men?
6. 6.The height of a projectile launched vertically upwards is given by h(t) = -4.9t² + 20t + 2, where h is in meters and t is in seconds. Calculate the average rate of change of the height from t = 1 second to t = 3 seconds. Then, find the instantaneous rate of change (velocity) at t = 2 seconds.