Precalculus Name: Chapter 1 Study Guide Period: ** Indicates Calculator OK 1.1: Linear Regression, Scatter Plots 1. If the following numerical data is a linear model, what is f(1)?

If you were to perform linear regression on your calculator using the table above, what could you predict about the correlation coefficient (r-value)?

2. Use your calculator to find the line of best fit. Show the window used to view the full scatter plot.**

Line of Best Fit: ___________________________________________ a. What does the slope represent?

b. What does the y-intercept represent?

c. Predict a reasonable test score for playing

video games for 12 hours. Is this interpolation or extrapolation?

d. If Brian received a 50 on his test, what is a reasonable number of hours he played video games for?

1.2: Properties of Functions 3. 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

4. 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.**

x -1 0 1 2

f(x) 2 3 5

Hours Playing

Video Games 6 7 9 5 8 10

Scores on Tests

85 77 75 75 80 65

1.3: The 11 Basic Functions (and Piecewise) 5. Which four of the eleven basic functions look the same as when they are reflected over the x-axis then the y-

axis? 6. Which of the 11 basic functions are even? Odd?

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

and determine its domain and range.

1.4: Function Composition

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

a) f + g b) f - g

9. 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

10. 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.

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

( )2

xg x

.

12. Graph the inverse of the following function. Then, find the rule (equation) to match the graphs. 1.6: Graphical Transformations

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

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

15. 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.

16. Identify the parent function and the transformations taking place (in order). Then, graph the function.

a. ( ) 2 4h x x b. ( ) 3 1j x x

c. 1( ) xf x e d.

31 1

( ) 12 2

g x x

A {quick} refresh of topics that COULD be included on the Chapter 1 Test

1.1: Analyzing Data Scatter Plots Linear Regression

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