Expresso
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expressions.docx1. Some of the steps we use to manipulate rational expressions or radical expressions are very different from the steps we use to manipulate linear expressions. Identify one of these steps and describe what makes it different from steps for linear expressions. Why is a new type of step necessary in this case? Give 3 examples.
2. Based on performing operations on rational expressions, solving rational equations and formulas, solving proportion and variation problems, solving problems involving radical expression, what types of real world problems typically require rational expressions to solve? Why are rational expressions necessary in these situations?
Please give 3 examples.
3. Solve for in the equation x2 - 2x - 35 = 0.
A. {-5, -7}
B. {5, -7}
C. {-5, 7}
D. {5, 7}
4. Consider the equations: and
. Select the solution for (f + g) (x).
A.
B.
C.
D.
5. Consider the equations: and
. Select the solution for (fg) (x).
A.
B.
C.
D.
6. Select the x-coordinate of the vertex of the parabola defined by the function f(x) = -7x2 + 3x +2.
A. -7/3
B. 2
C. 3/14
D. -3/7
7. Determine the equation of g(x) that results from translating the function f(x) = x2 + 3 upward 7units.
A. g(x) = (x + 10)2
B. g(x) = (x + 7)2 + 3
C. g(x) = x2 - 4
D. g(x) = x2 + 10
8. Determine the equation of g(x) that results from translating the function f(x) = (x + 8)2 to the right 13units.
A. g(x) = (x - 5)2
B. g(x) = (x + 21)2
C. g(x) = (x + 8)2 - 13
D. g(x) = (x + 8)2 – 13
9. Select the approximate values of x that are solutions to f(x) = 0, where f(x) = -5x2 + 6x + 9.
A. {–0.56, 0.67}
B. {-5, 6}
C. {–1.20, –1.80}
D. {–0.87, 2.07}
10. Select the approximate values of x that are solutions to f(x) = 0, where f(x) = -8x2 + 3x + 5.
A. {1.00, –0.63}
B. {-8, 3}
C. {–0.38, –0.63}
D. {–1.60, 0.60}
11. Select the approximate values of x that are solutions to f(x) = 0, where f(x) = -4x2 + 2x + 8.
A. {–1.19, 1.69}
B. {-4, 2}
C. {–0.50, –2.00}
D. {–0.50, 0.25}
E.
12. Solve for x in the equation x2 - 10x + 24 = 0.
A. {4, 6}
B. {-4, 6}
C. {4, - 6}
D. {-4, - 6}
13. If and
, which expression represents
for x >1?
A.
B.
C.
D.
14. Which of the following conclusions is true about the statement below?
A. The statement is true when x is negative.
B. The statement is always true.
C. The statement is never true.
D. The statement is true when x=0.
15.
A. 229.6 feet
B. 57.4 feet
C. 85.7 feet
D. 121.2 feet
16.
A. 2 < x ≤ 10
B. x > 20
C. x < 2
D. 10 ≤ x < 20
17.
A. Their vertices are maximums.
B. The graphs have the same shape with different vertices.
C. The graphs have different shapes with different vertices.
D. One graph has a vertex that is a maximum, while the other have a vertex that is a minimum.
18. Nancy made the following statement: The range of f(x) = ax + b is the set of all real numbers given that a and b are real numbers. Which produces a counter example to her statement?
A. b < 0
B. b = 0
C. a = 0
D. a < 0
