Name ________________________________ Period _____ Date ___________________
College Algebra
Chapter 2
Functions and Their Graphs
TEST RETAKE
A calculator may NOT be used on this test. Show all work and reasoning to receive full credit.
1) Determine if each of the following functions is even, odd, or neither. Then, state any symmetry that the graph
of each function might have. ( 3 points each)
(a) 𝑓(𝑥) = −4𝑥 3 + 2𝑥 2 − 5
(b) 𝑓(𝑥) = √3𝑥 6 − 5𝑥 2
2) Algebraically determine the domain of each of the following functions. Write each domain using set notation.
( 3 points each)
2𝑥+5
(a) 𝑓(𝑥) = 3𝑥 2 −𝑥−10
(b) 𝑓(𝑥) = √7 − 4𝑥
3) The point (25, 5) on f ( x )  x transformed according to 𝑓(𝑥) = −√5𝑥 + 10 − 6 would end up where?
( 2 points)
4) Consider this graph of 𝑓(𝑥) in order to answer the following questions. (1 point each)
(a) The domain of 𝑓(𝑥) is _________________________________ .
(b) The range of 𝑓(𝑥) is __________________________________ .
(0,0)
(4.5,0)
(c) This function increases over ____________________________ .
(-1,-2)
(d) This function decreases over ____________________________ .
(3,-4.5)
(e) The local maxima of 𝑓(𝑥) are __________________________ .
(f) The local minima of 𝑓(𝑥) are ______________________________________ .
(g) Over which interval(s) is 𝑓(𝑥) ≤ 0 ? _________________________________ .
(h) Over which interval(s) is 𝑓(𝑥) ≥ 0 ? _________________________________ .
(i) 𝑓(𝑥) = 4 for what value(s) of 𝑥 ? __________
(j) 𝑓(1) = __________
(𝑥 + 4)2 − 3, 𝑥 < −3
5) (a) Graph 𝑓(𝑥) = { 4,
𝑥 = −3
−2𝑥 − 4,
−3<𝑥 ≤1
on the Cartesian plane below.
(6 points)
(b) The domain of f(x) is ______________ . (1 point)
(c) f (-5) = ______ . (1 point)
(d) f (-3) = _______ . (1 point)
(e) What are the 𝑥 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡𝑠 of 𝑓(𝑥) ? (3 points)
(f) What is the 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 of 𝑓(𝑥) ? (1 point)
6) Graph each function and describe its transformation from its parent function. ( 5 points each)
(a) 𝑓(𝑥) = 2√−𝑥 + 4 − 5
(b) g ( x)  3 x  4  7
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