Functions and Graphs - Algebra - Lecture Notes, Study notes of Algebra

Functions and Graphs, Relation Represents, Domain and Range, Equations, Problems, Celsius Temperature, Fahrenheit Temperature, Fahrenheit Temperature Corresponding, Domain of the Functions, Difference Quotient are the key points of this lecture.

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2011/2012

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Lesson
Functions and Their Graphs
Determine whether the relation represents a function. If it is a function, state the domain and ran
g
e.
1) {(29, -2), (4, -1), (4, 0), (5, 1), (13, 3)}
Determine whether the followin
g
equations define
y
as a function of x:
2) y = |x|
3) x = y2
Find the value for the functions:
4) Find f(2) when f(x) = x2 - 8
x + 3 .
Find the value for the function.
5) Find f(-9) when f(x) = |x|- 6.
6) Find f(x - 1) when f(x) = 5x2 - 5x - 4.
Solve the problems:
7) If f(x) = 5x3 + 2x2 - x + C and f(-3) = 1, what is the value of C?
8) If f(x) = x - 3A
-3x + 5 and f(-3) = 9, what is the value of A?
9) The function F described by F(C) = 9
5C + 32 gives the Fahrenheit temperature corresponding to the
Celsius temperature C. Find the Fahrenheit temperature equivalent to 10°C.
Find the domain of the functions:
10) f(x) = x
x2 + 12
11) g(x) = 3x
x2 - 64
12) f(x) = 10 - x
CollegeAlgebra
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Lesson

Functions and Their Graphs

Determine whether the relation represents a function. If it is a function, state the domain and range.

Determine whether the following equations define y as a function of x:

2) y = |x|

3) x = y

Find the value for the functions:

4) Find f(2) when f(x) =

x2 - 8

x + 3

Find the value for the function.

5) Find f(-9) when f(x) = |x|- 6.

6) Find f(x - 1) when f(x) = 5x2 - 5x - 4.

Solve the problems:

7) If f(x) = 5x3 + 2x2 - x + C and f(-3) = 1, what is the value of C?

8) If f(x) =

x - 3A

-3x + 5

and f(-3) = 9, what is the value of A?

9) The function F described by F(C) =

C + 32 gives the Fahrenheit temperature corresponding to the

Celsius temperature C. Find the Fahrenheit temperature equivalent to 10°C.

Find the domain of the functions:

10) f(x) =

x

x2 + 12

11) g(x) =

3x

x2 - 64

12) f(x) = 10 - x

Find the domain of the function.

13) f(x) = 23 - x

Find the domain of the functions:

x

x - 2

Find and simplify the difference quotient of f,

f(x + h) - f(x)

h

, h≠ 0, for the functions:

15) f(x) = 9x + 9

16) f(x) =

4x

Solve the problem.

17) The function f(t) = -0.13t2 + 0.53t + 30.1 models the U.S. population in millions, ages 65 and older,

where t represents years after 1990. The function g(t) = 0.51t2 + 12.36t + 105.2 models the total

yearly cost of Medicare in billions of dollars, where t represents years after 1990. What does the

function

g

f

represent? Find

g

f

Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the

intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin.

-5 5 x

5 y

-5 5 x

5 y

Answer the question about the given functions:

19) Given the function f(x) = 2x2 - 4x - 2, is the point (1, -4) on the graph of f?

20) Given the function f(x) = x2 + 4x - 32, list the x-intercepts, if any, of the graph of f.

Answer Key

Testname: 7_FUNCTIONS_AND_GRAPHS

  1. not a function
  2. function
  3. not a function
    • 4 5
  4. 3
  5. 5x2^ - 15x + 6
  6. C = 115
  7. A = - 43
  8. 50°F
  9. all real numbers
  10. {x|x ≠ - 8, 8}
  11. {x|x ≤ 10}
  12. {x|x ≤ 23}
  13. {x|x > 2}
  14. 9
  15. -^1 4x (x + h)
  16. Cost per person in thousands of dollars. $6. thousand
  17. function domain: {x|x ≥ - 2} range: {y|y ≤ 0} intercepts: (-2, 0), (0, - 2), (2, 0) symmetry: none
  18. Yes
  19. (-8, 0), (4, 0)
  20. No