-Vocabulary and Core Concept Check 1. WRITING Describe the relationship between f(x) = x and all other nonconstant linear functions. 2. VOCABULARY Name four types of transformations. Give an example of each and describe how it affects the graph of a function. 3. WRITING How does the value of a in the equation y = flax) affect the Ayly = fox graph of y = f(x)? How does the value of a in the equation y = af(x) affect the graph of y = f(x)? y = g(x) 4. REASONING The functions f and g are linear functions. The graph of g is a vertical shrink of the graph of f. What can you say about the x-intercepts of the graphs of f and g? Is this always true? Explain. Monitoring Progress and Modeling with Mathematics In Exercises 5-10, use the graphs of f and g to describe 12. MODELING WITH MATHEMATICS The total cost the transformation from the graph of f to the graph C (in dollars) to cater an event with p people is of g. (See Example 1.) given by the function C(p) = 18p + 50. The set-up 5. g( x) = 1(x) + 2 6. fee increases by $25. The new total cost T is given g(x) = ((x + 4) by the function T(p) = C(p) + 25. Describe the transformation from the graph of C to the graph of T. ((x) - -2x Corey's Catering ((x ) = x - 3 Pricing 7. {(x) = ;x + 3; 8(x) = f(x) -3 $50 set-up fee + $18 per person 8. f(x) = - 3x + 4: 8(x) = f(x) + 1 9. f(x) = -x - 2: 8(x) = f(x + 5) In Exercises 13-16, use the graphs of f and h to describe 10. {(x) = 4x - 5;8(x) = f(x - 3) the transformation from the graph of f to the graph of h. (See Example 2.) 11. MODELING WITH MATHEMATICS You and a 13. ((x ) = x + 4 14. friend start biking from the same location. Your distance d (in miles) after MOX) - 1(-x) 1 minutes is given by the function d(1) = 1. Your friend starts biking 5 minutes after you. Your friend's A(x) = - 160 distance f is given by the function ((x) - -3x + 1 f(1) = d(1 - 5), Describe the transformation from the graph 15. f(x) = -5-x; h(x) =1(-x) of d to the graph of f. 16. (x) = ;x - 2; 1(x) = -5(x) Section 3.6 Transformations of Graphs of Linear Functions 151