Answers to
Practice with Functions
1. (a) Is a function because no value of x is repeated as a value of x.
(b) Is not a function because 3 is repeated as a value of x.
(c) Is not a function because 0 is repeated as a value of x.
(d) Is a function because no value of x is repeated as a value of x.
(e) Is not a function by the Vertical Line Test. (If any vertical line passes through the graph of a
relation more than once, then the relation is not a function.)
(f) Is a function by the Vertical Line Test. (No vertical line passes through the graph more than
once.)
(g) The graph of this function is a line with a slope of -2 and no vertical line would pass though it
more than once. So it is a function by the Vertical Line Test.
(h) The graph of this relation is a vertical line so a vertical line would pass through it more than
once. So this relation is not a function by the Vertical Line Test.
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2. (a) {1,2,3,4}
(b) {1,3,4}
(c) {-1,0,4}
(d) {-2,1,4,5}
(e) {x | −6 ≤ x ≤ 6} because the farthest to the left the graph goes is -6 and the farthest to the right the
graph goes is 6 and there is a point on the graph for every value of x between -6 and 6.
(f) {x | −5 ≤ x ≤ 7} because the farthest to the left the graph goes is -5 and the farthest to the right the
graph goes is 7 and there is a point on the graph for every value of x between -5 and 7.
(g) (−∞,∞) because the graph is a slanted line that goes forever to the left and forever to the right.
(h) {−4} because the only value of x that makes this relation true is -4.
3. (a) {1,2,3}
(b) {1,2,4,5}
(c) {0,2,4}
{-3}
(e) {y | −5 ≤ y ≤ 6} because the lowest the graph goes is -5 and the highest the graph goes is 6 and
there is a point on the graph for every value of y between -5 and 6.
(f) {y | −6 ≤ y ≤ −2} because the lowest the graph goes is -6 and the highest the graph goes is -2 and
there is a point on the graph for every value of y between -6 and -2.
(g) (−∞,∞) because the graph is a slanted line that goes down forever and up forever.
(h) (−∞,∞) because the graph is a vertical line that goes down forever and up forever.
4. (a) The relation is a function by the Vertical Line Test. (No vertical line passes through the graph
more than once.)
(b) [−9,8] because the farthest to the left the graph goes is -9 and the farthest to the right the graph
goes is 8 and there is a point on the graph for every value of x between -9 and 8.
(c) [−1,8] because the lowest point on the graph is -1 and the highest point on the 8 and there is a
point on the graph for every value of y between -1 and 8.
(d) When x is 3, the value of y is 4, so f (3) = 4.
(e) When x is -2, the value of y is 3, so f (−2) = 3 .
(f) There are three points on the graph that have a y value of 4. They are (-5,4), (-1,4), and (3,4). So
if f (x) = 4 , then x = -5, -1, or 3.
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(g) There is only one point on the graph that has a y value of 0. It is (7,0). So if f (x) = 0 , then x = 7.
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5. (a) When x = -2, y = 3 so f (−2) = 3 . (b) When x = 4, y = -2 so f (4) = −2 .
(c) Two ordered pairs have a y value of 3, (-2,3) and (3,3). So if f (x) = 3 , then x = -2 or 3.
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6. g(2) = −(2) 2 +1 €
= −4 +1 = −3
and
h(2) = 3(2) − 4 = 6€− 4 = 2
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so
g(2) + h(2) = −3 + 2 = −1.