Math 180EXAM 1Your Name______
Chapters 1 &2Aronne Spring 2011
NO CALCULATOR ON THIS PORTION OF THE TEST
Total points on the test = 129. Your grade will be figured out by doing: #correct / 129
1)Write the equations for the following graphs (8 points)
a) Vertically stretched by a factor of 2b) Vertically compressed by a factor of 0.2
Function y = ______Function y = ______
2)Sketch the graph (4 points)
Explain in words the transformations that took place. Sketch graph and label and “important” point in the graph
3)Write an equation for each of the following transformations of :(10 points)
a) has been shifted horizontally to the left 6 units.The new function is:y =
b) has been shifted vertically down 4 units. The new function is:y =
c) has been reflected about the x-axis. The new function is:y =
d) has been vertically compressed. A possible function is: y =
e) has been vertically stretched. A possible function is:y =
Math 180EXAM 1Your Name______
Chapters 1 &2Aronne Spring 2011
CALCULATORS are OK
SHOW ALL WORK
4)Write the standard form for the following circle:(8 points)
Write the center of the circle.______
Write the radius of the circle.______
On the grid above, sketch the axes and the circle.
5)Use algebra to find the y-intercepts of the circle shown in problem 1. If there aren’t any, you must explain how the algebra steps lead to that answer. (6 points)
6)If find the difference quotient in simplified form.(6 points)
Notice that in the difference quotient formula, h
7)Complete the following blanks indicating what kind of symmetry: (12 points)
(Y- symm. , x- symm. , or origin symmetry)
An EVEN function has ______symmetry.
An ODD function has ______symmetry.
b) If , the function is even / odd(circle one).
If , the function is even / odd (circle one)
c) Make up an even function and write it here: (include at least two terms!!!!)
e) Make up an odd function and write it here: (include at least two terms!)
8)Give the domain of the following functions. In each case, show procedure or reasoning.(8 points)
a) (use inequalities)b) (use interval notation)
9)Let (Simplify your answers if possible)
(12 points)
a) /c. / d. Give the domain of
10)The following data represent the population of unknown bacteria when an antibacterial solution has been applied to the culture of bacteria. (6 points)
Find the average rate of change of the population from 0 to 3 hours. Interpret within context.
11)Write a rational function with domain all real numbers. (3 points)
12)An open box is to be made from a rectangular piece of cardboard 24 inches by 36 inches by cutting out a square from each corner and turning up the sides. Note: include units whenever appropriate.
(16 points)
a) Express the volume V of the box as a function of the length x of the side of the square cut from each corner. DO NOT MULTIPLY. There is no time for that.
b) Specify the RESTRICTED domain of the Volume function. This will help you with the window selection.
c) Sketch the graph with the calculator and find the optimal value of x that should be cut in order to obtain a box with the largest volume. Show sketch, label axes with variable names, and units. Label maximum point.
d) What is the largest volume?
e) What are the dimensions of the box with largest volume? Show work
Length = ______Width = ______Height = ______
Organize your neat work and label parts a-e below
13)Use your graphing calculator to graph the function: (10 points)
Answer all questions using the calculator:
- Show a complete graph of the function.What window values did you use?
- Give all local maximum and local minimum points.
- Give the values of the x-intercepts(s) and the y-intercept(s).
- Approximate over what intervals the function is increasing, decreasing or constant.
- Determine ALGEBRAICALLY if the function is even, odd, or neither. Show your work
- Write the domain.
- Write the range.
Organize your neat work and label parts a-g below
14)Given the following piece-wise defined function:(8 points)
Evaluate each of the following – do not graph. Show work!
a) f(-4) =b) f(9) =c) f(-7) =
d) What is the domain of this function?
15)The intersection points between the graph of the linear function G(x) and the graph of the quadratic function F(x) are the points (5, 5) and (11.2, 6.24). Use the graph to solve the inequality. F(x) > G(x) Label important information in the graph. Write answer in interval notation. (6 points)
16)If you have time, sketch the graph of problem 14. Think and graph, you should not need a calculator to do this. Indicate clearly the coordinates of the endpoints. (6 points)