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.
Problem 1 Solve the inequality. Write the solution on a number line.
2x2 - 5x > 3
Solve x1/2 + 2x1/4 - 8 = 0
Graph the following and label the important features:
Answer the following True or False. If True, explain your reasoning, if False, explain your reasoning or show a counter-example.
A. All parabolas y = ax2 + bx + c (a non zero) are graphs of functions.
B. If the vertex of the parabola y = ax2 + bx + c has positive y-coordinate and the parabola is concave up, then the parabola has two x-intercepts.
C. If a graph has two y-intercepts then the graph is not the graph of a function.
Problem 5 Let f(x) = 3x + 2, g(x) = x + 3, and c(x) = -1. Find
A) f ° g (x)
f(x + h) - f(x)
D) c ° f (2)
Problem 6 Consider the function
f(x) = 3x - 2
A. Sketch the graph of f(x) and explain in a complete sentence why the graph indicates that f(x) has an inverse function.
B. Find (algebraically) f -1 (x).
Problem 7 (16 Points) Graph the quadratic function. Label any intercepts, the vertex, and the axis of symmetry. State the domain and range.
y = -2x2 + 4x + 6
Problem 8 The
graphs of y = f(x) and y =
g(x) are given below. Find
C. f -1 (0)
D. g ° f (1)
Extra Credit: Write down one thing that your instructor can do to make the class better and one thing that you feel that the instructor should continue doing.
(Any constructive remarks will be worth full credit.)