Precalculus Name: Chapter 1 Study Guide Period: ** Indicates Calculator OK 1.2: Properties of Functions 1. Find the domain of the following:

a. 2 4

( )3

xh x

x

b. ( ) 4 3f x x c. 2

1( )

7 10

xg x

x x

2. Find all local and absolute maxima and minima of the function: 4 3( ) 3 2 3h x x x x . Then, find the

intervals where the function is increasing, decreasing and constant.** 1.3: The 11 Basic Functions (and Piecewise) 3. Which four of the eleven basic functions look the same as when they are reflected over the x-axis then the y-

axis? 4. Which of the 11 basic functions are even? Odd?

5. Graph the function 𝒇(𝒙) = {−𝒙𝟐 + 𝟓, 𝒙 ≤ 𝟐𝟐𝒙 − 𝟓, 𝒙 > 𝟐

and determine its domain and range.

1.4: Function Composition

6. If 2( ) 1f x x and ( ) 3g x x , find each of the following and specify the domain.

a) f + g b) f - g

7. If 2( ) 9f x x and ( )g x x , find each of the following and specify the domain.

a) f(g(x)) b) g(f(x))

1.5: Inverse of Functions

8. Find the inverse of 3( ) 5 2f x x algebraically. State the domain of the inverse including any restrictions

inherited from the original function. Hint: to find the range, think of the parent function and transformations taking place.

9. Confirm algebraically that the following two functions are inverses: 3( ) 2 5f x x and 35

( )2

xg x

.

10. Graph the inverse of the following function. 1.6: Graphical Transformations

11. Identify the parent function and the transformations taking place (in order): 3( ) 4( 2) 7f x x .

Parent Function: _______________ HORIZONTAL VERTICAL 1) ________________________ 1) ________________________ 2) ________________________ 2) ________________________ 3) ________________________ 3) ________________________

12. Describe the transformations applied to ( )f x x to get the function ( ) 2 3g x x .

Parent Function: _______________ HORIZONTAL VERTICAL 1) ________________________ 1) ________________________ 2) ________________________ 2) ________________________ 3) ________________________ 3) ________________________

13. Identify the parent function and the transformations taking place (in order): ( ) 2 4h x x

Parent Function: _______________ HORIZONTAL VERTICAL 1) ________________________ 1) ________________________ 2) ________________________ 2) ________________________ 3) ________________________ 3) ________________________

14. Identify the parent function and the transformations taking place (in order): ( ) 3 1j x x

Parent Function: _______________ HORIZONTAL VERTICAL 1) ________________________ 1) ________________________ 2) ________________________ 2) ________________________ 3) ________________________ 3) ________________________

15. Identify the parent function and the transformations taking place (in order): 1( ) xf x e

Parent Function: _______________ HORIZONTAL VERTICAL 1) ________________________ 1) ________________________ 2) ________________________ 2) ________________________ 3) ________________________ 3) ________________________

16. Identify the parent function and the transformations taking place (in order):

31 1

( ) 12 2

g x x

Parent Function: _______________ HORIZONTAL VERTICAL 1) ________________________ 1) ________________________ 2) ________________________ 2) ________________________ 3) ________________________ 3) ________________________

17. If 3( )f x x , write a function rule for each of the following transformations.

a. A horizontal stretch by a factor of 3 and a vertical translation up 1 unit.

b. A vertical stretch by a factor of 2, and a horizontal translation left 1 unit.

18. Below are graphs of the 12 basic functions. Use them to answer the next set of questions.

a. Which basic functions are one-to-one?

b. Which basic functions are ODD? EVEN?

c. Which basic functions are increasing on their entire domain?

d. Which basic functions are their own inverse?

19. Use the graph of f(x) at the right to answer the questions below. a. 𝐥𝐢𝐦

𝒙→−𝟒−𝒇(𝒙) =

b. 𝐥𝐢𝐦

𝒙→−𝟒+𝒇(𝒙) =

c. 𝐥𝐢𝐦

𝒙→−𝟒𝒇(𝒙) =

d. 𝐥𝐢𝐦

𝒙→−𝟏𝒇(𝒙) =

e. 𝐥𝐢𝐦

𝒙→∞𝒇(𝒙) = f. Is f(x) continuous at x=2?

A {quick} refresh of topics that COULD be included on the Chapter 1 Test 1.2: Properties of Functions Function vs. Relation (graphically, from equation) Domain (graphically, algebraically) Range (graphically) Increasing/Decreasing/Constant Boundedness Extrema Even/Odd/Neither

1.3: 11 Basic Functions Properties & Graphs of all 11 functions Piecewise Functions

1.4: Function Composition

Adding, Subtracting Functions (and the resulting domain)

Composing Functions (and the resulting domain) 1.5: Inverses of Functions Finding the inverse of a function:

o Graphically o Algebraically

Proving two functions are inverses 1.6: Graphical Transformations Identifying transformations on a parent function, in

order Writing an equation from a transformation Graphing transformations of a parent function