ANSWER KEY
Algebra II | LESSON 1-2 Parent functions day 2
Additional Vocabulary Support
Check students’ graphs. The x-intercept is (5.5, 0).
Check students’ graphs. The y-intercept is (0, –2.2).
Check students’ graphs. There are two lines of symmetry, y = x – 7 and y = –x + 3.
(–∞, 5) and (5, ∞)
(–∞, –2) and (–2, ∞)
Check students’ graphs. The equations of the asymptotes are y = –2 and x = 5.
As the absolute value of x increases, the y-values get closer and closer to y = –2.
As the absolute value of y increases, the x-values get closer and closer to x = 5.
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8. y =
x
9. domain: (−∞, 0) and (0, ∞); range: (−∞, 0) and (0, ∞); intercepts: none;
minimum and maximum on interval [–2, 4]: both undefined
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10.
domain: (−∞, ∞); range: (−∞, ∞); x-intercept: (1, 0); y-intercept: (0, –1);
minimum and maximum on interval [–2, 4]: –3 and 3, respectively
11. domain: (−∞, ∞); range: (−∞, ∞); x- and y-intercept: (0, 0);
minimum and maximum on interval [–2, 4]: –4 and 8, respectively
12. domain: (−∞, ∞); range: [0, ∞); x- and y-intercept: (0, 0);
minimum and maximum on interval [–2, 4]: 0 and 32, respectively
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13. domain: (−∞, ∞); range: (−∞, ∞); x-intercept: ( , 0); y-intercept: (0, 4);
minimum and maximum on interval [–2, 4]: –8 and 10, respectively
14. An asymptote is a line that a graph approaches as x or y increases in absolute value. A
graph that approaches an asymptote has asymptotic behavior.
15. A function can have a slope of 0 and still have attributes of symmetry. A linear function
with a slope of 0 (i.e., y = b) is a horizontal line with reflectional symmetry across any
vertical line.
16. A domain of (−∞, ∞) means that the domain consists of all real numbers.
17. False; it has neither an x- nor a y-intercept.
18. False; the range does not include the value y = 0.
19. false
20. No; the domain of a function, by definition, includes only those values of the
independent variable for which the function is defined.
21. The minimum value of a function is the minimum value of the dependent variable over
its entire range or, if the minimum is requested for a specific set of values of the
independent variable, the minimum value of the corresponding set of values of the
dependent variable.
22. It exhibits reflectional symmetry about the axis.
23. The function exhibits no asymptotic behavior over its domain, 0 ≤ x ≤ 20. Also, the
function has neither reflectional nor rotational symmetry over its domain. The
minimum and maximum values of the function are 0 and 12, respectively,
corresponding to the endpoints of the range of the function, 0 ≤ y ≤ 12. The y-intercept
of the function is (0, 12), and the x-intercept is (20, 0).