Section 2.6 Graphs of Basic Functions
(continued)
217
28. (a) The equation can be rewritten as 2 y x 2 3 y 1 x 2 2 3 .2 x can be any real number. Because the square of any real number is not negative, 2 1 x 2 is never negative. Taking the constant term into consideration, range would be 3, . 2
domain: , ; range:
6
1
(b) Each value of x corresponds to just one value of y. x 4 y 6 represents a function. 1 y 4 1x 2 3f x x 23 4 1 4
2
3 2
2 2
1 2
1
3
2
26. (a) The equation can be rewritten as y 2 5 x. y can be any real number. Because the square of any real number is not negative, y 2 is never negative. Taking the constant term into consideration, domain would be 5, . domain: 5, ; range: , (b) Because (−4, 1) and (−4, −1) both satisfy the relation, y 2 x 5 does not represent a function. 2
27. (a) x 2 y 2 25 is a circle centered at (−2, 0) with a radius of 5. The domain will start 5 units to the left of –2 and end 5 units to the right of –2. The domain will be [−2 − 5, 2 + 5] = [−7, 3]. The range will start 5 units below 0 and end 5 units above 0. The range will be [0 − 5, 0 + 5] = [−5, 5]. (b) Because (−2, 5) and (−2, −5) both satisfy 2
the relation, x 2 y represent a function.
2
2
3
4y x 6 y 4 x 4 y 4 x 2 . x can be any real number, so the domain is all real numbers and the range is also all real numbers. domain: , ; range: ,
f 2
,
(b) Each value of x corresponds to just one value of y. x 2 2 y 3 represents a
25. (a) The equation can be rewritten as 1
3
25 does not
function. y 1 2x 2 3 f2 x f2
1
Section 2.6
2
2 3 1 2
1
4
x2
3 2
3 4 3 1 2 2
2 2
2
2
2
Graphs of Basic Functions
2 1. The equation f x x
matches graph E.
The domain is , . 2. The equation of f x x
matches graph G.
The function is increasing on 0, . 3. The equation f x
x3 matches graph A.
The range is , . 4. Graph C is not the graph of a function. Its equation is x y 2 . 5. Graph F is the graph of the identity function. Its equation is f x x. 6. The equation f x x matches graph B. f 1.5 1 3 7. The equation f x x matches graph H. No, there is no interval over which the function is decreasing.
8. The equation of f x
x matches graph D.
The domain is 0, . 9. The graph in B is discontinuous at many points. Assuming the graph continues, the range would be {…, −3, −2, −1, 0, 1, 2, 3, …}.
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