math worksheet
iikotu
quiz_4.docxMATH 107 Quiz 4
Name Click here to enter text.
Each question is worth 5 points. Questions 1 – 5 are multiple choice; you do not need to show your work. Short answers for Questions 6 – 10; show your work to earn full credit – highlight answers in yellow or draw a box around the answer. You can insert additional lines if needed.
Leave answers in exact form unless otherwise directed to approximate the results. Write all fractions in lowest form and round decimals to hundredths. Write answers using positive exponents except when using scientific notation. Simplify all radicals and rationalize the denominators. Write complex numbers in the form a + bi. Applied problems must have the variables identified and an equation for full credit.
MULTIPLE CHOICE Check the box of the one alternative that best completes the statement or answers the question.
1.) Graph f(x) = -x2 - 2x – 7. Four graphs are in order of the multiple choice.
☐ First graph
☐ Second graph
☐ Third graph
☐ Fourth graph
☐ None of these
2.) Graph the function, showing all asymptotes (those that do not correspond to an axis) as dashed lines. List the x- and y-intercepts. Four graphs are in order of the multiple choice.
☐ x-intercept: (7, 0) , y-intercept: (0, 7) (first graph)
☐ x-intercept: (3, 0) , y-intercept: (second graph)
☐ x-intercept: (-3, 0) , y-intercept: (third graph)
☐ x-intercept: (0, 0) , y-intercept: (0, 0) (fourth graph)
☐ None of these
3.) Simplify. Write your answers in the form of a+bi, where a and b are real numbers.
☐ 1036 + 416i
☐ -44 + 56i
☐ 100 i
☐ 100
☐ None of these
4.) Find an equation of variation if y varies directly as z, and y = 27 when z = 189.
☐
☐ y = 7z
☐ y = -2z
☐ y = - ½ z
☐ None of these
5.) Find a rational function that satisfies the given conditions: vertical asymptotes x = -4, x = -1.
☐
☐
☐
☐
☐ None of these
3
Short answers. You must show your work to earn full credit. Highlight answers in yellow or draw a box around the answer.
6.) Write your answers in the form of a + bi, where a and b are real numbers:
7.) Use the quadratic formula to find the exact solutions: x2 + 35 = 5x.
8.) A rectangular garden has dimensions of 23 feet by 10 feet. A gravel path of equal width is to be built around the garden. How wide can the path be if there is enough gravel for 234 square feet?
9.) Determine whether there is a maximum or minimum value for the given function, and find that value: f(x) = -3x2 - 30x – 76.
10.) Solve for p: (4p - 5)2 = 5(4p - 5) + 6.
11.) In Exercises 1 - 20, show that the given function is one-to-one and find its inverse. Check your answers algebraically and graphically. Verify that the range of f is the domain of f −1 and vice-versa.
