# MATH 0303

COURSE REVIEW for FINAL EXA

Find the domain of each of the functions.

1)

For the function represented in the graph,

determine the domain.

2)

Find the function value.

3) Find f (x −1) when f (x) = 5x^{2} − 3x + 7

For the given functions f and g, find the requested

function.

4) f (x) = 4x − 7 ; g (x) = 2x − 9 Find f ยท g

Find the indicated composite for the pair of functions.

5) Given f (x) = 4x^{2} + 3x + 4 and

g (x) = 3x − 7 , find (g o f )(x) .

6) Given f (x) = x^{2} +1 and g (x) = 2x +1,

find ( f o g )(4)

The function f is one-to-one. Find its inverse.

Find the x- and y- intercepts of the function.

For the function represented in the graph, determine the domain.

9)

The graph of a function f is given.

10) Find the value(s) of x for which f (x) = −1

Solve the following inequalities and write the solution in interval notation.

Solve the following rational inequalities and write the solution in interval notation.

Solve the following and write the solution in interval notation or set notation.

Graph the following system of linear inequalities.

Simplify the radicals and add or subtract as indicated.

Rationalize the denominator.

Divide the complex number. Write the answer in the form a + bi

Solve the following radical equation.

Use the laws of exponents to simplify. Do not use negative
exponents in your answer and assume all

variables represent positive real numbers.

Use the laws of exponents to simplify and write as a single radical.

Graph.

Solve.

Use the discriminant to determine the number and type of solutions.

Solve.

41) In 2004 the population of Corsica had an annual growth
rate that could be

modeled by the function A(t) = 886,000(1.0107)^{t} .

Use this model to predict the population in 2050. Round to the nearest thousand.

42) The normal pH level for streams and rivers is between 6.5 and 8.5. A high

level of bacteria in a particular stream caused environmentalists to test the

water. The level of ions was found to be 0.006 mol/L.

What is the pH level of the stream?

(use pH = −log[H ^{+} ] , where [H^{+} ] represents the concentration of hydrogen

in moles per liter.)

Graph the functions.