University:
Carleton College
Course:
MATH 120 | Calculus 2
Academic year:

2024
Views:

343

Pages:

3
Author:

Nevaeh Bauer

Question 1 Which of the functions is not a piecewise defined function? a) sign function b) rectangle function c) trigonometric function d) floor function e) parent function of absolute value Answer Floor function is not piecewise defined function, because it is a continuous function. Therefore, the answer is (d). Question 2 Tell whether each of the following functions is an odd function, an even function, or neither. a) The sum of two even functions b) The sum of two odd functions c) The sum of an even function and odd one d) The product of two even functions e) The product of two odd functions f) The product of an even function and odd function Answer a) The sum of two even functions is an even function b) The sum of two odd functions is an odd function c) The sum of an even function and odd one is neither even nor odd d) The product of two even functions is an even function e) The product of two odd functions is an even function f) The product of an even function and odd function is an odd function Question 3 Give the examples of these functions a) linear function b) power function c) exponential function d) quadratic function e) polynomial function of degree 5 f) rational function Answer a) linear function: y = 3x + 2 b) power function: f(x) = x² c) exponential function: f(x) = aˣ d) quadratic function: f(x) = 2x² + 3x + 1 e) polynomial function of degree 5: f(x) = 2x⁵ - x⁴ + x³ - 2x² - 3 f) rational function: f(x) = (2x⁴ - x² + 1) / (x² - 4) Question 4 Match the function with its name: f(x) = x³ a) squaring function b) square root function c) cubic function d) linear function e) constant function f) absolute value function g) greatest integer function h) reciprocal function i) identity function Answer The function f(x) = x³ is called a cubic function. Its domain and range are set of real numbers. Thus, the correct answer is (c). Question 5 Name the function f(x) = 1/x Answer 1 The function f(x) = 1/x is called a reciprocal function. Its range is the set of positive real numbers excluding zero, since division by zero is not defined and its domain is the set of real numbers. Answer 2 To solve the function f(x) = 1/x, we need to find the value of x for which f(x) equals a specific value. Let's say we want to find the value of x when f(x) = a, where a is a constant. We can start by setting up the equation: 1/x = a To solve for x, we can multiply both sides of the equation by x: 1 = ax Now, we can isolate x by dividing both sides by a: x = 1/a Therefore, the solution to the equation f(x) = 1/x when f(x) = a is x = 1/a Answer 3 The function can be represented as f(x) = 1/x. To solve this function, we need to find the values of x for which f(x) is defined. Since division by zero is undefined, we know that x cannot be equal to zero, so we have x ≠ 0. To find the inverse of the function, we can solve for x in terms of f(x): y = 1/x Multiply both sides by x to isolate x on one side: yx = 1 Divide both sides by y to solve for x: x = 1/y Therefore, the inverse function f⁻¹(x) is given by: f⁻¹(x) = 1/x In conclusion, the function f(x) = 1/x is defined for all x except x = 0, and its inverse function is f⁻¹(x) = 1/x.