Practice Exam 1

Please work out each of the given problems.  Credit will be based on the steps that you show towards the final answer.  Show your work.

Key

Problem 1  Solve the inequality.  Write the solution on a number line.

2x2 - 5x > 3

 

Problem 2  Solve the inequality.  Write the solution on a number line.

(4x-3)/(x+5) <= 0

 

Problem 3  Solve

x1/2 - 2x1/4 - 8  =  0

 

Problem 4  Solve

root(x-3) + x = 3 


Problem 5 The graph of y = x2 + 2 is shown below.  Find the equation of the other parabola.

 

Problem 6  Find the domain of

f(x) = (x^2 - 5x - 1) / (x^3 - 3x^2 + 2x)

Problem 7  Solve the following system of equations

3x - 2y  + 4z = 1
2x +  y -  5z  = 3
4x - 5y + 13z = -1

 

Problem 8  One muffin, two pies, and three cakes costs $23.  One muffin, three pies, and two cakes cost $21.  One muffin, four pies and five cakes costs $39.  Find the cost of each.

 

Problem 10  Graph the piecewise defined function.  Then use the graph to determine the domain and range of the function.

f(x) = {x+1 if x < 2, 5-2x if x >=2

 

Problem 11  Consider the graph of y = f(x) shown below.

Graph of y = f(x) through (-1,1), (0,1), (1,-1), (2,1)

A.  Find f(2)

B.  Find all values of x such that f(x) = 1.

 

Problem 12  Answer the following true or false.  If true, explain your reasoning.  If false, explain your reasoning or provide a counter example.

A.  If a graph has two y-intercepts, the graph is not the graph of a function of y in terms of x.

B.  If (1,5) and (2,5) are two ordered pairs of a relation, then the relation cannot be a function.

C.  The graph of y = f(x+1) + 2 is the same as the graph of y = f(x) but shifted one to the right and two upwards.