135 Study Guide

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  • Topic: Function, Injective function, Domain of a function
  • Pages : 9 (1732 words )
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  • Published : May 6, 2013
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Math 135 Final Exam Study Guide The graph of a function is given. Follow the directive(s). 1) y 5 (0.5, 2)

(3.5, 2) 5 (6, -1.1) x

-5

(-5, -3) (-4, -3) -5

(a) List all the intervals on which the function is increasing. (b) List all the intervals on which the function is decreasing. (c) List all the intervals on which the function is constant. (d) Find the domain. (e) Find the range. (f) Find f(-5). (g) Find f(6). (h) Find x when f(x) = 0. (i) Find the x-intercept(s). (j) Find the y-intercept(s).

Find the value for the function. 2) Find f(3) when f(x) = x2 - 3x + 6. 3) Find f(-2) when f(x) = x2 - 9 . x+3

4) Find f(-9) when f(x) = |x|- 6. Determine whether the relation represents a function. If it is a function, state the domain and range. 5) Bob Ann Dave carrots peas squash

1

6) Bob Ann Dave Ms. Lee Mr. Bar

Find the domain of the function. 3x 7) g(x) = x2 - 1 8) f(x) = x2 x2 + 1 4-x

9) f(x) =

For the given functions f and g, find the requested function and state its domain. 10) f(x) = 7 - 6x; g(x) = -9x + 6 Find f + g. 11) f(x) = 6 - 2x; g(x) = -4x + 2 Find f + g. 12) f(x) = 4x - 2; g(x) = 8x - 3 Find f - g. 13) f(x) = 8x - 6; g(x) = 2x - 5 Find f - g. 14) f(x) = 5x + 1; g(x) = 3x - 1 Find f œ g. 15) f(x) = 5x + 3; g(x) = 4x + 8 Find f œ g. 16) f(x) = 5x + 4; g(x) = 4x - 3 f Find . g 17) f(x) = 5x + 3; g(x) = 4x - 5 f Find . g

2

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. 18) 5 y

-5

5 x

-5

19)
10 y

5

-10

-5

5

x

-5

-10

Graph the function. 20) f(x) = -x + 3 2x - 3 if x < 2 if x ≥ 2 y 5

-5

5

x

-5

3

21) f(x) = x+5 -8 -x + 5 if -8 ≤ x < -2 if x = -2 if x > -2 y 10 5

-10

-5 -5 -10

5

10

x

Find the indicated composite for the pair of functions. 22) (f † g)(x): f(x) = 6x + 9, g(x) = 5x - 1 23) (f † g)(x): f(x) = 3x + 10, g(x) = 3x - 1 24) (g † f)(x): f(x) = 4x2 + 2x + 7, g(x) = 2x - 8 25) (g † f)(x): f(x) = 4x2 + 2x + 6, g(x) = 2x - 7 Follow the directive(s). 26) Find and simplify the difference quotient of f, f(x + h) - f(x) , h ≠ 0, for the given function: f(x) = x 2 - 7x - 2 h

27) Find and simplify the difference quotient of f,

f(x + h) - f(x) , h ≠ 0, for the given function: f(x) = x 2 + 6x + 4 h

4

28) f(x) = -x2 - 2x + 8
y 10 5

-10

-5 -5

5

10

x

-10

For the given function above, (a) Find the vertex. (b) Find the x- and y- intercepts. (c) Find the axis of symmetry. (d) Graph the function.

29) f(x) = x2 - 2x - 3
y 10 5

-10

-5 -5 -10

5

10

x

For the given function above, (a) Find the vertex. (b) Find the x- and y- intercepts. (c) Find the axis of symmetry. (d) Graph the function.

5

The graph of a function f is given. Use the horizontal line test to determine whether f is one-to-one. 30) y 10

-10

10

x

-10

31)
y 10

-10

10

x

-10

If the following defines a one-to-one function, find the inverse. 32) f(x) = 5x + 2 33) f(x) = x2 - 2 34) f(x) = 2 x-2

Solve the equation. Find all real solutions. 1 + 2x 35) 2 = 32 7 - 3x 1 36) 4 = 16 37) log9 (x - 2) + log9 (x - 2) = 1 38) log (x - 3) = 1 - log x Find the domain of the function. 39) f(x) = log (x - 10)

6

40) f(x) = log (x - 8) Solve the problem. 41) A rumor is spread at an elementary school with 1200 students according to the model N = 1200(1 - e-0.16d) where N is the number of students who have heard the rumor and d is the number of days that have elapsed since the rumor began. How many students will have heard the rumor after 5 days? 42) If $5,000 is invested for 6 years at 5%, compounded continuously, find the future value. Compute the amount in m years if a principal P is invested at a nominal annual interest rate of r compounded as given. Round to the nearest cent. 43) P = $1,000, m = 8, r = 11% compounded annually 44) P = $1,000, m = 9, r = 12% compounded semiannually 45) P = $480, m = 5,...
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