:enVision Algebra 1 10-1 Additional Practice 7:. .............. .'i The Square Root Function Find the domain and range for each square root function. State the x and y-intercepts, if they exist. 1. f(x) = m 2. g(X) = W; 4 3. h(x) = J)??? + 3 Domain: '. Domainiiiw _. Domainzw-..\" Range:.....' , Range: 31....\" Range; ' Xintercept: xintercept: gal/.42\".-- xintercept: .,-._...W yintercept: .3; z-...;......m., yinterce pt: WWW. ..... WWWWW wwwwwww W... yintercept: jar-;:',;g.....;W. Graph each function by translating f(x) = R. 4. g(X):J3?+3 5. h(X)=\\/X+ 2 6.k(x)=Jx-3+1 " 7' i y" y i i' i .4er r _. 7. How does the average rate of change for a square root function behave, for intervals of fixed lengths over the domain, as the endpoints of the intervals increase? EXp'ain' 1+ DC CFCQS 85 8. The distance d in miles to the horizon when looking out at the ocean is - modeled by the function d = J1.5a, where a is the altitude in feet where you are standing. Round your answer to the nearest whole mile. a. if you are standing at an altitude of 150 feet, at what distance can you see the horizon? [5 ml! [65 b. if the distance to the horizon is 30 miles, at what altitude are you standing? 600 13+ enVisionTM Algebra 1 0 Teaching Resources genVision Algebra l 10-4 Reteach to Build Understanding " Translations of Functions 1. Complete the phrases so they correctly describe the equations, by filling in the blanks with variables or words. 900 = f(X) + k Translate the graph of 7',\"me units my? mm 9(X) = f(X) k . Translate the graph of f ML\" units mpavu MMW 9(X) = f(X h) Translate the graph of f Whm_ units WEQEL mmmmmmmm 9(X) = f(X + h) Translate the graph of fmlgw units mmgl 2. Ryan made an incorrect statement about g(x) = f(X 5) + 7. Put an X next to the incorrect statement and correct his error. The graph of g is translated up 7 units and right 5 units. When f(x) = x2, the function g(x) = (X 5)2 + 7. When f(x) = 2", the function g(x) = (2" ~ 5).+ '7. , When f(X) = J7, the function g(x) = m + 7. 3. Complete the statements about the graphs of g and f. y f(x) = IXI f( ) 9(X) =12l I ___{: The graph of fis translated horizontally f units _ JI O 4 { l ' , and vertically' l ,,,,,,, units . _ . ( ) enVisionTM Algebra 1 0 Teaching Resources Name zenVIslon' Algebra} 10-4 Additional Practice Translations of Functions Describe the effect of each translation of f for the given function. 1. g(x) = f(x) + 8 2. h(X) = f(x 11) Sketch the graph each function. 4. f(x) : (x 2)2 4 y l 5. g(X)=\\/X+4+3 3. j(x) = f(x+ 7) 4 I x E savvasrealize.com 6. h(X) = 2X+4 'T y L... :41 _.L 7. A rational function is of the form f(x) = a Where x is nonzero and a is a nonzero constant. What is an equation for a rational function translated 7! h units horizontally and k units vertically? i i 8. Three athletic clubs offer different membership costs. The first club charges $20 per month. The second club charges $20 per month plus an application fee of $10. The third club charges $20 per month and offers a $15.00 reduction in the first month's membership fees. Write the equations that model the total cost of membership at the three clubs. Describe how the second and third graphs are related to the graph of the first club. enVisionTM Algebra 1 - Teaching Resources