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College Algebra Test
9. Answer each of the following questions concerning the
graph to the lower right.
(a) Determine the range and domain of the function f from its graph, given
to the right below. Use interval notation.
Solution:
Domain = [−3, 3]
Range = [ 0, 2]
(b) State the intervals of increase and decrease.
Interval of increase = [−3, 0]
Interval of decrease = [ 1, 3]
10. The graph of the function y = x^2 is shifted
horizontally 2 units to the left, and shifted 4 units vertically upwards.
Write the equation of the resulting function:
11. Sketch each of the following graphs using transformation methods .
Solution: 
(b) g(x) = x + 1. Solution: 
12. Solve the absolute inequality : 1 − 2x ≥ 6
Solution: We have, again,
1 − 2x ≥ 6 

1 − 2x ≥ 6  or  1 − 2x ≤ −6 
−2x ≥ 5  or  −2x ≤ −7 
x ≤ −5/2  or  x ≥ 7/2 
The solution set is (−∞,−5/2) ∪ [7/2,∞)
13. Answer each of the following concerning piecewisedefined function
(a) (2 pts) Calculate each of the following :
f (4)= −3
f (−3) = 9
(b) (4 pts) Graph the function on the axis to the right.
Be
sure to indicate the value of the function at x = 0 on
the graph.
14. Let f (x) = 2x^2 − x and g(x) = 3x + 1, perform the following compositions.
15. Consider the functionFind functions f and g such that
16. Solve the following system using the elimination method . Leave your answer as a solution set.
Solution Set ={(1/2, 1/3)}
Solution: We use the elimination method:
2x + 3y = 2  (1)  
4x − 3y = 1  (2)  
4x + 6y = 4  (3)  multiply (1) by 2 
4x − 3y = 1  (2)  copy of equation (2) 
9y = 3  (4)  subtract (2) from (3) 
y = 1/3  (5)  solve 
2x + 3(1/3) = 2  substitute (5) into (1)  
x = 1/2  solve!  
The solution set is { (1/2, 1/3) } 
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