Study Skills Exercise. Review Exercises. Concept 1: Linear and Constant Functions

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1 Section. Graphs of Functions Section. Boost our GRADE at mathzone.com! Stud Skills Eercise Practice Eercises Practice Problems Self-Tests NetTutor e-professors Videos. Define the ke terms. a. Linear function b. Constant function c. Quadratic function d. Parabola Review Eercises. Given: g,,,,,,, a. Is this relation a function? b. List the elements in the domain. c. List the elements in the range.. Given: f 7,,,,, a. Is this relation a function? b. List the elements in the domain. c. List the elements in the range.. Given: f a. Evaluate f, f, f, and f, if possible. b. Write the domain of this function in interval notation.. Given: g a. Evaluate g(), g(), g(), and g(), if possible. b. Write the domain of this function in interval notation.. The force (measured in pounds) to stretch a certain spring inches is given b f. Evaluate f() and f(), and interpret the results in the contet of this problem. 7. The velocit in feet per second of a falling object is given b Vt t, where t is the time in seconds after the object was released. Evaluate V() and V(), and interpret the results in the contet of this problem. Concept : Linear and Constant Functions. Fill in the blank with the word vertical or horizontal. The graph of a constant function is a line. 9. For the linear function f m b, identif the slope and -intercept.

2 Chapter Introduction to Relations and Functions. Graph the constant function f. Then use. Graph the linear function g. the graph to identif the domain and Then use the graph to identif the domain and range of f. range of g. g Concept : Graphs of Basic Functions For Eercises 7, sketch a graph b completing the table and plotting the points.. f. g f() f() g(). h. k h() k(). q 7. p q() 9 p()

3 Section. Graphs of Functions 7 Concept : Definition of a Quadratic Function For Eercises 9, determine if the function is constant, linear, quadratic, or none of these.. f 9. g. k 7. h. m. n.. p. Q. t 7. r. w 9. T Concept : Finding the - and -Intercepts of a Function Defined b f ( ) For Eercises 7, find the - and -intercepts, and graph the function.. f. f. g. h 9. f. g 7. g 7. h

4 Chapter Introduction to Relations and Functions For Eercises, use the function pictured to estimate a. The real values of for which f. b. The value of f f() f() f()... f() f() f() For Eercises, a. Identif the domain of the function. b. Identif the -intercept of the function. c. Match the function with its graph b recognizing the basic shape of the function and using the results from parts (a) and (b). Plot additional points if necessar.. q. p. 7. k. r 9.. f. g.. h h s k i. ii. iii. iv.

5 Section. Graphs of Functions 9 v. vi. vii. viii. i.. Concept : Determining Intervals of Increasing, Decreasing, or Constant Behavior For Eercises 7, give the open interval(s) over which the function is a. increasing b. decreasing c. constant.. g() k(). 7. p() h() For Eercises, refer to the graphs of the si basic functions (see page ). For each function, give the open interval(s) over which the function is a. increasing b. decreasing c. constant. f 9. g. h. m ƒ ƒ. n. p

6 9 Chapter Introduction to Relations and Functions. Refer back to the graph in Eercise. The function is increasing on the interval,. Suppose we arbitraril select two values of on this interval such as and. Is it true that g g? How does this relate to the definition of a function increasing on an interval?. Refer back to the graph in Eercise. The function is decreasing on the interval,. Suppose we arbitraril select two values of on this interval, such as. and.. Is it true that k. 7 k.? How does this relate to the definition of a function decreasing on an interval? Graphing Calculator Eercises For Eercises 7, use a graphing calculator to graph the basic functions. Verif our answers from the table on page.. f 7. f. f 9. f 7. f 7. f Section. Concepts. Definition of Direct and Inverse Variation. Translations Involving Variation. Applications of Variation Variation. Definition of Direct and Inverse Variation In this section, we introduce the concept of variation. Direct and inverse variation models can show how one quantit varies in proportion to another. Definition of Direct and Inverse Variation Let k be a nonzero constant real number. Then the following statements are equivalent:.. varies directl as. is directl proportional to. varies inversel as. is inversel proportional to. f k f k Note: The value of k is called the constant of variation. For a car traveling mph, the equation d t indicates that the distance traveled is directl proportional to the time of travel. For positive values of k, when two variables are directl related, as one variable increases, the other variable will also increase. Likewise, if one variable decreases, the other will decrease. In the equation d t, the longer the time of the trip, the greater the distance traveled. The shorter the time of the trip, the shorter the distance traveled.

7 Chapter Introduction to Relations and Functions Skill Practice. Graph f b first making a table of points.. Graph h ƒ ƒ b first making a table of points. For our reference, we have provided the graphs of si basic functions in the following table. Summar of Si Basic Functions and Their Graphs Function Graph Domain and Range. f Domain, Range,. Domain, Range,. Domain, Range,. f Domain, Range, Skill Practice Answers. f (). f() h() h(). Domain,. Range, Domain,, Range,, The shapes of these si graphs will be developed in the homework eercises. These functions are used often in the stud of algebra. Therefore, we recommend that ou associate an equation with its graph and commit each to memor.