4.5: Chapter 4 Review

PROBLEM SET: CHAPTER 4 REVIEW

Functions and Function Notation (4.1)

1. Consider the set of points ${3,5), (5,4), (2,9), (0,5), (7,9)}$.
   1. Find the domain.
   2. Find the range.
   3. Do these points represent a function?
2. For the function $f(x)=-x^{2}-8$, evaluate each of the following.
   1. $f(3)$
   2. $f(-3)$
3. For the function $g(x)=-3x+4$, evaluate each of the following.
   1. $g(2)$
   2. $g(x)+2$
   3. $g(x)+2$

Understanding the Basic Functions (4.2)

4. Without relying on technology, sketch a graph with at least 3 points of each of the following functions.
   1. $f(x)=x^{3}$
   2. $f(x)=|x|$
   3. $f(x)=x$
   4. $f(x)=\sqrt{x}$
   5. $f(x)=c$
   6. $f(x)=\dfrac{1}{x}$
   7. $f(x)=x^{2}$
5. Given the function $f (xt ) = \left\{ \begin{array} { l l } { 5x-7 } & { \text { if } x \leq -1 } \\ { -2x^{2} + 5 } & { \text { if } x > 0 } \end{array} \right.$, find each of the following values.
   1. $f(-4)$
   2. $f(-1)$
   3. $f(3)$

Transformations of Functions (4.3)

6. For each function below, identify the basic function, describe the transformations, and sketch a graph of the transformed function.
   1. $f(x)=\sqrt{x+9}$
   2. $g(x)=\dfrac{1}{x}-2$
   3. $h(x)=|x-4|+3$
   4. $j(x)=-x^{2}-8$
7. For each function shown below, identify the basic function, describe the transformations, and find an equation for the function.
   1.  
   2. 

Quadratic Functions and Their Applications (4.4)

8. How can you determine the direction of the graph of $f(x)=-3x^{2}+5x-4$ without even graphing it?
9. Use Desmos to find the following characteristics of $g(x)=2x^{2}-8x+3$.
   1. Vertex
   2. Axis of symmetry
   3. y-intercept
   4. x-intercepts
   5. Domain
   6. Range
10. The daily profit for a manufacturing company is modeled by the function $P(x)=-0.6x^{2}+168x-9375$, where $x$ is the number of items manufactured.
    1. What is the company's profit if zero items are manufactured in a day?
    2. What is the company's profit if 90 items are manufactured in a day?
    3. What is the range of items that must be made each day in order to make any profit?
    4. What is the maximum daily profit they can make, and how many items do they need to manufacture in order to make that profit?
    5. What do the x-intercepts of the graph represent in this scenario?