PROBLEMS ON POLYNOMIAL FUNCTIONS PRECALCULUS

Problem 1 :

Evaluate the function at the given value of the independent variable and simplify.

f(x) = x² - 5 ; f(x - 4)

Solution

Problem 2 :

Use the graph to find the indicated function value.

y = f(x), Find f(-2)

Solution

Problem 3 :

Use the graph to determine the function's domain and range.

Solution

Problem 4 :

Use the graph of the given function to find any relative maxima and relative minima. State where f(x) increases and decreases.

f(x) = x³ - 3x² + 1

Solution

Problem 5 :

Find and simplify the difference quotient [f(x + h) - f(x)]/h, h ≠ 0 for the given function.

f(x) = x² + 7x + 3

Solution

Problem 6 :

Use the given conditions to write an equation for the line in slope - intercept form.

Passing through (2, 5) and (1, 8)

Solution

Problem 7 :

Begin by graphing the standard quadratic function f(x) = x². Then use transformations of this graph to graph the given functions.

g(x) = -1/2 (x + 2)² + 3

Solution

Problem 8 :

For the given functions f and g, find the indicated composition.

(f ∘ g) (x)

Solution

Problem 9 :

Find the inverse of the one-to-one function.

f(x) = 3/(2x + 1)

Solution

Problem 10 :

Complete the square and write the equation in standard form. Then give the center and radius of the circle.

x² - 10x + 25 + y² - 8y + 16 = 64

Solution

Answer Key

1)   f(x - 4) = x² + 11 - 8x

2)  f(-2) = 2

3)  Domain = [0, ∞) Range = [-1, ∞)

4)  f(x) is increases in (-∞, 0) ∪ (2, ∞)

f(x) is decreases in (0, 2)

5)  h + 2x + 7

6)  y = -3x + 11

7)  Reflection about x-axis, vertical shrink with the factor of 1/2 units, horizontal translation of 2 units left and vertical translation of 3 units up.

8)  (f ∘ g) (x) = 35x/(20x + 4)

9)  f^-1(x) = (3/2x) - (1/2)

10)  Center = (5, 4), radius = 8