CalculusChapter 1 Review

I can graph transformations of all of the major parent functions.

I can graph piecewise functions.

I can graph transformations of all 6 trigonometric functions.

I can find the domain and range of any function given either an equation or a graph.

23) Find the domain and range of #2, 3, 7, 11, 13, 14, 17, 18, 21,

17) ��� y = −4 − cosπ x

22) ��� y = 12cot x − 2π

3⎛⎝⎜

⎞⎠⎟

25) State the domain and range of:

���

7) ��� f x( ) = − 1x + 2

− 5

2) ��� f x( ) = − 45x + 2 + 3

19) ��� y = −2sec 3x − 3π4

⎛⎝⎜

⎞⎠⎟

12) ��� f x( ) = −2 −x +1 − 69) ��� f x( ) = 3− x+2 + 3

4) ��� y = −2 ⋅ 15

⎛⎝⎜

⎞⎠⎟x−1

− 3

16) ��� y = 3cos 2x5

+π⎛⎝⎜

⎞⎠⎟

21) ��� y = cot π x2

+π⎛⎝⎜

⎞⎠⎟ + 3

1) ��� y = 3− 2(4 − x)2

6) ��� y = 14x −1( )3 + 2

13) ��� f x( ) = −3x + 7 x < 2− x − 4 + 2 x > 2

⎧⎨⎪

⎩⎪

11) ��� y = 9 − x2

18) ��� y = 12csc x

2− π3

⎛⎝⎜

⎞⎠⎟ + 2

3) ��� y = − 132 − x +1

8) ��� x − 3( )2 + y +1( )2 = 16

15) ��� y = −2sin6x − 3

20) ��� y = 23tan x + π

4⎛⎝⎜

⎞⎠⎟ −1

14) ��� g x( ) =− 12x + 4( )2 + 5 −6 ≤ x < −1

−2 −1≤ x < 34 x + 3 − 2 3≤ x < 6

⎧

⎨

⎪⎪⎪

⎩

⎪⎪⎪

5) ��� f x( ) = log6 x + 4( )− 5

24) State the domain and range of:

���

10) ��� y = −3ln x −1( )+ 2

I can find a requested composition of functions.

I can use function composition to verify a given equation is the inverse of a given function.

38) Verify your answers to #30, 31 using composition of functions.

I can use the properties of logarithms and exponents.

40) Simplify. ���2 x−3y4( )−22x−1y5z( )2

37) ��� f ! f( ) x( )

41) Condense into a single logarithm.

���3ln x − ln x + 3( )+ 2 ln y

34) ��� h! g( ) x( )

39) Simplify. ��� 5x2z6( )3 5x2yz−2( )−3

35) ��� f g x( )( )

For 34-37, use ��� , ��� , and ��� . Find…f x( ) = 2 + 5x5x − 2

g x( ) = 9 − x2 h x( ) = x2 − 9

42) Expand the logarithm.

��� logx −1( )3y2z

36) ��� f g h x( )( )( )

I can algebraically determine if a function is even, odd, or neither.

I can find the inverse of a given function both algebraically and graphically.

27) ��� f x( ) = x3

8 + x228) ��� f x( ) = ex2

31) Find the inverse and determine if the inverse is a function.

��� y = 5 + 2 log3 x + 5( )

29) ��� f x( ) = sin x + π2

⎛⎝⎜

⎞⎠⎟

32) Graph the inverse of the given function.

���

26) ��� f x( ) = x2 − 2x − 3

30) Find the inverse and determine if the inverse is a function.

��� .y = x + 32x − 7

33) Graph the inverse of the given function.

���

I can find and use an appropriate exponential model to represent a problem situation.

44) The number of bacteria in a culture is increasing according to the law of exponential growth. The initial population is 250 bacteria, and the population after 10 hours is double the population after 1 hour. How many bacteria will there be after 6 hours?

45) Estimates of the amounts (in billions of dollars) of U.S. online advertising spending from 2011 through 2015 are shown in the table below. Find an exponential model that approximates the data.

Year 2011 2012 2013 2014 2015 Advertising Spending 31.3 36.8 41.2 45.5 49.5

According to this model, when will the amount of U.S. online advertising spending reach $80 billion?

I can solve basic equations using the properties of logs and exponents.

I can solve basic trigonometric equations.

46) ���52 = 24e3x−1 + 7

50) ��� 4sin2 x + 7 = 9; 0 ≤ x < 2π

47) ���50 = 2 9( )−5 x+4 − 4

53) ��� tan x( ) cos x −1( ) sin x +1( ) = 0; 0 ≤ x < 2π

48) ���−6 = −3log9x4+ 2⎛

⎝⎜⎞⎠⎟

43) The half-life of radioactive actinium ��� is 21.77 years. What percent of a present amount of radioactive actinium will be left after 19 years?

227Ac( )

51) ��� 4cos2 x − 3= 0; −∞ < x < ∞

49) ���−5 = logx 8 + 2

52) ��� 2sin x −1( ) cos x( ) = 0; −π ≤ x < π