MATH 041 Lecture Notes - Lecture 2: Imaginary Number, Negative Number

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1 Sep 2016

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A function is a relation from a set a to a set b that assigns each x- element in a exactly with a y-element in b. Relation 1 { (3,5) , (4,2) , (7,6) } Relation 2 { (2,3) , (6,1) , (5,4) } Relation 3 { (2,1) , (2,2) , (3,6) } Not a function, because a function cannot have 2 points with the same. Vertical line test x2 + y = 3; this is a function x2 + y2 = 25; not a function because this makes a circle. Function notation f(x) = function f" is evaluated at x. Difference quotient f(x + h) f(x) / h, example: f(x) = 3x-7. 3(x+h) 7 (3x 7) / h. 3x + 3h 7 3x + 7 / h. |a| = { a if a >= 0. The domain of the function is the collection of all possible x values.

Related Questions

Can someone please help me with this? I don't even think the ones I answered are correct.

Determine whether therelation is a function.

{(-2, -7), (3, -5), (6, -4), (9,-6), (10, -1)}

A) Not a function
B) Function

Determine whether therelation is a function.

{(-5, -4), (-2, 9), (-1, -2),(-1, 7)}

A) Function
B) Not a function

Determine whether therelation is a function.

{(-7, -1), (-7, 2), (-1, 8), (3,3), (10, -7)}

A) Not a function
B) Function

Determine whether therelation is a function.

{(1, -3), (1, 1), (6, -8), (9,-3), (11, -3)}

A) Not a function
B) Function

Determine whether therelation is a function.

{(-6, -9), (-2, 1), (1, -1), (7,-7)}

A) Not a function
B) Function

Determine whether theequation defines y as a function of x.

x + y = 9

A) y is a function ofx
B) y is not a function of x

Determine whether theequation defines y as a function of x.

x² + y² =1

A) y is a function ofx
B) y is not a function of x

Determine whether theequation defines y as a function of x.

x = y²

A) y is a function ofx
B) y is not a function of x

Evaluate the functionat the given value of the independent variable and simplify.

f(x) = -3x - 8; f(-2)

A) 14
B) -11
C) -2
D) 22

10.

Evaluate the functionat the given value of the independent variable and simplify.

f(x) = x² - 1; f(x -2)

A) x² + 4
B) x² - 4x + 3
C) x² - 3
D) x² - 4x + 4

11.

Evaluate the functionat the given value of the independent variable and simplify.

f(x) = 4x² + 5x - 6;f(x - 1)

A) -3x² + 4x -7
B) 4x² - 3x - 7
C) 4x² - 3x + 3
D) 4x² - 19x + 3

12.

Evaluate the functionat the given value of the independent variable and simplify.

f(x) = ; f(5)

A)
B)
C)
D)

13.

Find the slope of theline that goes through the given points.

(3, -5), (-9, -8)

A) -
B)
C)
D) 4

14.

Find the slope of theline that goes through the given points.

(-7, 6), (-7, -9)

A) Undefined
B)
C) 0
D) -

15.

Find the slope of theline that goes through the given points.

(-1, 4), (5, 4)

A)
B) 0
C) 2
D) Undefined

16.

Find the slope of theline that goes through the given points.

(-2, -6), (-9, -17)

A)
B)
C) -
D)

17.

Find the slope of theline that goes through the given points.

(-8, 8), (-5, 2)

A)
B)
C) -
D) - 2

18.

Find the slope of theline that goes through the given points.

(-3, -7), (9, -7)

A) 0
B) 1
C) -4
D) 4

19.

Use the givenconditions to write an equation for the line in point-slopeform.

Slope = 4, passing through (-3,7)

A) y - 7 = 4(x + 3)
B) y = 4x - 19
C) x - 7 = 4(y + 3)
D) y + 7 = 4(x - 3)

20.

Use the givenconditions to write an equation for the line in point-slopeform.

Slope = , passing through (8,7)

A) x - 7 = (y - 8)
B) y - 7 = (x - 8)
C) y + 7 = (x + 8)
D) y = x + 8

Algebra

Please notice that some questions have multiple parts, i.e. a-cor a-d.

Given f(x) = 3x2 - 2 and g(x) = 3 - 1/2 x2: find the following expressions. (f.g)(4) (g f)(2) (f.f)(l) (g.g)(0) (f . g)(4) = (Simplify your answer.) find the following expressions, (f.g)(4) (g.f)(2) (f.f)(l) (g.g)(0) (fog)(4) = (Type an exact answer, using radicals as needed. Simplify your answer.) Given f(x) = |x| and g(x) =9/x2+3, find the following expressions. (f.g)(4) (g f)(2) (f.f)(l) (g.g)(0) (f . g)(4) = (Type an integer or a simplified fraction.) For the function on the right determine whether the function is one-to-one. Is the function one-to-one? Yes No For the function below, determine whether the function is one-to-one. {(7,7),(8,8),(9,46),(10,51)} Is the function one-to-one? Yes No For the function below, determine whether the function is one-to-one. {(7,7),(8,8),(9,46),(10,51)} Is the function one-to-one? Yes No The graph of a function f is given. Use the horizontal-line test to determine whether f is one-to-one. Is f one-to-one? Choose the correct answer below. No Yes The graph of a function f is given. Use the horizontal-line test to determine whether f is one-to-one. Is f one-to-one? Choose the correct answer below. No Yes Find the inverse of the one-to-one function. State the domain and range of the inverse function. {(10,-8), (-13,-10), (-9,2), (-8,11), (-10,1)} Which of the following is the inverse function? {(-10,1), (-8,11), (-9,2), (-13,- 10), (10,-8)} {(-8,10), (-10,-13), (2,-9), (11,-8), (1,-10)} {(-8,-10), (-10,-8), (2,-9), (11,-13), (1,10)} {(-10,8), (13,10), (9,-2), (8,-11), (10,-1)} Consider the functions f(x) = - 3x + 7 and g(x) = -1/3(x - 7). Find f(g(x)). Find g(f(x)). Determine whether the functions f and g are inverses of each other. What is f(g(x))? f(g(x)) = (Simplify your answer.) Consider the functions f(x) = 3x - 15 and g(x) = x/3 + 5. Find f(g(x)). Find g(f(x)) Determine whether the functions f and g are inverses of each other. What is f(g(x))? f(g(x)) = (Simplify your answer.) Match the graph to one of the following functions. y = 6x y = 6-x y = -6x y = -6-x y = 6x_ 1 y = 6x-1 Which function is represented by the graph? (Type A, B, C, D, E, F, G, or H.) Begin with the graph of y = ex and use transformations to graph the following function. Determine the domain, range, and horizontal asymptote of die function. f(x) = 8e-x Choose the correct graph below. Solve the equation. 4x.2x2=162 x = (Use a comma to separate answers as needed.) If 4-x = 5;what does 42x equal? 42x = (Type a reduced fraction.)

Show transcribed image text Given f(x) = 3x2 - 2 and g(x) = 3 - 1/2 x2: find the following expressions. (f.g)(4) (g f)(2) (f.f)(l) (g.g)(0) (f . g)(4) = (Simplify your answer.) find the following expressions, (f.g)(4) (g.f)(2) (f.f)(l) (g.g)(0) (fog)(4) = (Type an exact answer, using radicals as needed. Simplify your answer.) Given f(x) = |x| and g(x) =9/x2+3, find the following expressions. (f.g)(4) (g f)(2) (f.f)(l) (g.g)(0) (f . g)(4) = (Type an integer or a simplified fraction.) For the function on the right determine whether the function is one-to-one. Is the function one-to-one? Yes No For the function below, determine whether the function is one-to-one. {(7,7),(8,8),(9,46),(10,51)} Is the function one-to-one? Yes No For the function below, determine whether the function is one-to-one. {(7,7),(8,8),(9,46),(10,51)} Is the function one-to-one? Yes No The graph of a function f is given. Use the horizontal-line test to determine whether f is one-to-one. Is f one-to-one? Choose the correct answer below. No Yes The graph of a function f is given. Use the horizontal-line test to determine whether f is one-to-one. Is f one-to-one? Choose the correct answer below. No Yes Find the inverse of the one-to-one function. State the domain and range of the inverse function. {(10,-8), (-13,-10), (-9,2), (-8,11), (-10,1)} Which of the following is the inverse function? {(-10,1), (-8,11), (-9,2), (-13,- 10), (10,-8)} {(-8,10), (-10,-13), (2,-9), (11,-8), (1,-10)} {(-8,-10), (-10,-8), (2,-9), (11,-13), (1,10)} {(-10,8), (13,10), (9,-2), (8,-11), (10,-1)} Consider the functions f(x) = - 3x + 7 and g(x) = -1/3(x - 7). Find f(g(x)). Find g(f(x)). Determine whether the functions f and g are inverses of each other. What is f(g(x))? f(g(x)) = (Simplify your answer.) Consider the functions f(x) = 3x - 15 and g(x) = x/3 + 5. Find f(g(x)). Find g(f(x)) Determine whether the functions f and g are inverses of each other. What is f(g(x))? f(g(x)) = (Simplify your answer.) Match the graph to one of the following functions. y = 6x y = 6-x y = -6x y = -6-x y = 6x_ 1 y = 6x-1 Which function is represented by the graph? (Type A, B, C, D, E, F, G, or H.) Begin with the graph of y = ex and use transformations to graph the following function. Determine the domain, range, and horizontal asymptote of die function. f(x) = 8e-x Choose the correct graph below. Solve the equation. 4x.2x2=162 x = (Use a comma to separate answers as needed.) If 4-x = 5;what does 42x equal? 42x = (Type a reduced fraction.)

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MATH 041 Lecture Notes - Lecture 2: Imaginary Number, Negative Number

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