# 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 piecewise-defined 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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