Does the table or equation represent a linear or nonlinear function? Explain.

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1 Chapter Review Dnamic Solutions available at BigIdeasMath.com. Functions (pp. 0 0) Determine whether the relation is a function. Eplain. Ever input has eactl one output. Input, Output, 5 9 So, the relation is a function. Determine whether the relation is a function. Eplain.. (0, ), (5, 6), (7, 9).. Input, Output, The function = represents the amount (in dollars) of mone in our bank account after ou babsit for hours. a. Identif the independent and dependent variables. b. You babsit for hours. Find the domain and range of the function.. Linear Functions (pp. 0). Does the table or equation represent a linear or nonlinear function? Eplain. a As increases b, increases b different amounts. The rate of change is not constant. So, the function is nonlinear. b. = The equation is in the form = m + b. So, the equation represents a linear function. Does the table or graph represent a linear or nonlinear function? Eplain The function = 60 8 represents the amount (in dollars) of mone ou have after buing movie tickets. (a) Find the domain of the function. Is the domain discrete or continuous? Eplain. (b) Graph the function using its domain. 6 Chapter Graphing Linear Functions

2 . Function Notation (pp. 6) a. Evaluate f() = 9 when =. f() = 9 Write the function. f() = () 9 Substitute for. = 6 9 Multipl. = Subtract. When =, f() =. b. For f() =, find the value of for which f() =. f() = Write the function. = Substitute for f(). = Divide each side b. When =, f() =. Evaluate the function when =, 0, and f() = g() = Find the value of so that the function has the given value. 0. k() = 7; k() = 9. r() = 5 ; r() = 9 Graph the linear function.. g() =. h() = +. Graphing Linear Equations in Standard Form (pp. 9 ) Use intercepts to graph the equation + = 6. Step Find the intercepts. To ind the -intercept, substitute To ind the -intercept, substitute 0 for and solve for. 0 for and solve for. + = 6 + = 6 + (0) = 6 (0) + = 6 = = Step Plot the points and draw the line. The -intercept is, so plot the point (, 0). The -intercept is, so plot the point (0, ). Draw a line through the points. (0, ) (, 0) 5 Graph the linear equation.. 8 = 6 5. = 6 6. = 5 7. = 6 Chapter Chapter Review 65

3 .5 Graphing Linear Equations in Slope-Intercept Form (pp. 5 ) a. The points represented b the table lie on a line. How can ou find the slope of the line from the table? What is the slope of the line? Choose an two points from the table and use the slope formula. Use the points (, ) = (, 7) and (, ) = (, ). slope = = ( 7) The slope is. = 9, or b. Graph + =. Identif the -intercept. Step Rewrite the equation in slope-intercept form. = + Step Find the slope and the -intercept m = and b = Step The -intercept is. So, plot (0, ). Step Use the slope to ind another point on the line. slope = rise run = Plot the point that is units right and unit up from (0, ). Draw a line through the two points. (0, ) The line crosses the -ais at (, 0). So, the -intercept is. The points represented b the table lie on a line. Find the slope of the line Graph the linear equation. Identif the -intercept.. = = 0. + = 9. A linear function h models a relationship in which the dependent variable decreases units for ever units the independent variable increases. Graph h when h(0) =. Identif the slope, -intercept, and -intercept of the graph. 66 Chapter Graphing Linear Functions

4 .6 Transformations of Graphs of Linear Functions (pp. 5 5) a. Let f() = +. Graph t() = f( ). Describe the transformation from the graph of f to the graph of t. The function t is of the form = f( h), where h =. So, the graph of t is a horizontal translation units right of the graph of f. 5 t() = f( ) f() = + b. Graph f() = and g() =. Describe the transformations from the graph of f to the graph of g. Note that ou can rewrite g as g() = f(). Step There is no horizontal translation from the graph of f to the graph of g. Step Stretch the graph of f verticall b a factor of to get the graph of h() =. Step Relect the graph of h in the -ais to get the graph of r() =. Step Translate the graph of r verticall units down to get the graph of g() =. g() = f() = Let f() = +. Graph f and h. Describe the transformation from the graph of f to the graph of h. 5. h() = f( + ) 6. h() = f() + 7. h() = f( ) 8. h() = f() 9. h() = f() 0. h() = f(6). Graph f() = and g() = 5 +. Describe the transformations from the graph of f to the graph of g. Chapter Chapter Review 67

5 .7 Graphing Absolute Value Functions (pp. 55 6) Let g() = + +. (a) Describe the transformations from the graph of f() = to the graph of g. (b) Graph g. a. Step Translate the graph of f horizontall unit left to get the graph of t() = +. Step Stretch the graph of t verticall b a factor of to get the graph of h() = +. Step Relect the graph of h in the -ais to get the graph of r() = +. Step Translate the graph of r verticall units up to get the graph of g() = + +. b. Method Step Make a table of values. 0 g() g() = + + Step Plot the ordered pairs. Step Draw the V-shaped graph. Method Step Identif and plot the verte. (h, k) = (, ) Step Plot another point on the graph such as (0, ). Because the graph is smmetric about the line =, ou can use smmetr to plot a third point, (, ). Step Draw the V-shaped graph. g() = + + (, ) (, ) (0, ) Graph the function. Compare the graph to the graph of f() =. Describe the domain and range.. m() = + 6. p() =. q() = 5. r() = 6. Graph f() = + and g() = +. Compare the graph of g to the graph of f. 7. Let g() =. (a) Describe the transformations from the graph of f() = to the graph of g. (b) Graph g. 68 Chapter Graphing Linear Functions

6 Chapter Test Determine whether the relation is a function. If the relation is a function, determine whether the function is linear or nonlinear. Eplain = +. = Graph the equation and identif the intercept(s). If the equation is linear, find the slope of the line.. = 6 5. =.5 6. = Find the domain and range of the function represented b the graph. Determine whether the domain is discrete or continuous. Eplain Graph f and g. Describe the transformations from the graph of f to the graph of g. 9. f() = ; g() = + 0. f() = ; g() = +. Function A represents the amount of mone in a jar based on the number of quarters in the jar. Function B represents our distance from home over time. Compare the domains.. A mountain climber is scaling a 500-foot cliff. The graph shows the elevation of the climber over time. a. Find and interpret the slope and the -intercept of the graph. b. Eplain two was to ind f(). Then ind f() and interpret its meaning. c. How long does it take the climber to reach the top of the cliff? Justif our answer.. Without graphing, compare the slopes and the intercepts of the graphs of the functions f() = + and g() = f(). Elevation (feet) Mountain Climbing f() = Time (hours). A rock band releases a new single. Weekl sales s (in thousands of dollars) increase and then decrease as described b the function s(t) = t 0 + 0, where t is the time (in weeks). a. Identif the independent and dependent variables. b. Graph s. Describe the transformations from the graph of f() = to the graph of s. Chapter Chapter Test 69