Interactive multiple-choice quiz: Inverse Relations and Functions
Explore the mathematical concept of inverse relations and functions. Learn how to verify if two relations are inverses by checking if their ordered pairs are swapped, analyzing tables of values, and reflecting graphs across the line y=x. This set of practice problems also covers determining the domain and range of inverse functions and the procedural steps to find an inverse algebraically.
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اختبار شهادة تدريبي مؤقت للصف والمادة والفصل نفسه.
اختر إجابة واحدة لكل سؤال. عند الاختيار ستظهر النتيجة فورًا: الأخضر صحيح، والأحمر خطأ، وسيظهر تفسير الإجابة مباشرة إن كان متوفرًا. وبعد آخر سؤال ستظهر الدرجة النهائية تلقائيًا.
An inverse function swaps the x and y coordinates. While most points match, f(x) has (-3, -2), which should map to (-2, -3) in its inverse, but g(x) contains (2, 3) instead.
In these sets, every ordered pair (x, y) in f(x) is swapped to (y, x) in g(x), which is the definition of an inverse relation.
Question 3
DB ID: 1316
Points: 1
Given the tables for f(x) and g(x): f(x) points: (1, 0), (3, -3), (5, 7), (-9, -2) g(x) points: (0, 1), (-3, -3), (7, 5), (-2, -9) Are the relations inverses?
Explanation
To be inverses, all points must be swapped. For f(x), the point (3, -3) should map to (-3, 3) in the inverse, but g(x) has the point (-3, -3).
Question 4
DB ID: 1317
Points: 1
Are the graphs inverses?
Explanation
The graphs are reflections of each other across the line y = x, indicating they are inverse functions.
Question 5
DB ID: 1318
Points: 1
Are the graphs inverses?
Explanation
The graphs are not reflections across the line y = x. They appear to be reflections across the x-axis with a vertical shift, which does not represent an inverse relationship.
Question 6
DB ID: 1319
Points: 1
Are the graphs inverses?
Explanation
The curves are symmetrical with respect to the line y = x, confirming they are inverses.
Question 7
DB ID: 1320
Points: 1
Are the graphs inverses?
Explanation
The two functions graphed show a clear reflection over the identity line y = x.
Question 8
DB ID: 1321
Points: 1
Given the set {(3, 2), (-4, 1), (0, -8), (5, -2)}, which of the following points is part of the inverse?
Explanation
To find the inverse, you swap the x and y coordinates of each point. The point (3, 2) becomes (2, 3).
Question 9
DB ID: 1322
Points: 1
Given the set {(3, 4), (-2, 1), (-6, -7), (-3, -2), (0, -1)}, what is the DOMAIN of the INVERSE function?
Explanation
The domain of an inverse function is the same as the range of the original function. The range of the given set is {4, 1, -7, -2, -1}.
Question 10
DB ID: 1323
Points: 1
Given the function represented by these points: (4, -4), (3, 7), (1, 0), (-5, -2). What is the RANGE of the INVERSE function?
Explanation
The range of the inverse function is identical to the domain of the original function. The x-values of the original function are {4, 3, 1, -5}.
Question 11
DB ID: 1324
Points: 1
TRUE OR FALSE: If the DOMAIN of a function is (-∞, 2], then the DOMAIN of the INVERSE function will also be (-∞, 2].
Explanation
This is false because the domain of the inverse function is equal to the range of the original function, not its domain.
Question 12
DB ID: 1325
Points: 1
TRUE OR FALSE: If the RANGE of a function is (4, 2], then the DOMAIN of the INVERSE function will also be (4, 2].
Explanation
This is true by definition: the range of a function always becomes the domain of its inverse.
Question 13
DB ID: 1326
Points: 1
Here is the domain and range for a function: D: (-∞, ∞) R: [3, ∞) What is the domain and range of the inverse?
Explanation
To find the domain and range of the inverse, you swap the domain and range of the original function.
Question 14
DB ID: 1327
Points: 1
What is the inverse quadratic function?
Explanation
The inverse of the squaring operation x2 is the square root operation, expressed as ±√x to account for both branches.
Question 15
DB ID: 1328
Points: 1
How do you find an inverse?
Explanation
The standard algebraic method for finding an inverse relation or function is to swap the roles of the independent variable (x) and the dependent variable (y).
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