MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Transcription

1 Eam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Begin b graphing the standard quadratic function f() =. Then use transformations of this graph to graph the given function. ) h() = ( + ) - ) Given functions f and g, perform the indicated operations. ) f() = -, g() = - - Find f g. )

2 ) f() = - 7, g() = + Find fg ) Determine whether the equation defines as a function of. ) = - + is a function of is not a function of ) Use the graph of f to draw the graph of its inverse function. ) )

3 Find a polnomial equation with real coefficients that has the given roots. ) i, -i + + = 0 - = = 0 + = 0 ) Find the equation that the given graph represents. 7) 0 7) - -0 f() = - + f() = f() = f() = Divide using snthetic division. ) ) Find the inverse of the one-to-one function. 9) f() = 7 + f-() = 7-7 f-() = 7 + f-() = 7-7 f-() = 7-7 9) Graph the function. + if -7 < ) f() = - if = - + if > )

4 (, ) (, ) (, ) (, ) (-7, ) - (, -) (-7, -) - (, -) - - (, ) (, ) (, ) (, ) (-7, -) - (, -) (-7, ) - (, -) - - Use the given conditions to write an equation for the line in the indicated form. ) Passing through (, ) and perpendicular to the line whose equation is = + 7; point-slope form ) - = ( - ) = = - ( - ) - = ( + ) ) Passing through (, ) and parallel to the line whose equation is = - + ; slope-intercept form = - 7 = = = ) Use Descartesʹs Rule of Signs to determine the possible number of positive and negative real zeros for the given function. ) f() = ) or positive zeros, or 0 negative zeros or 0 positive zeros, or negative zeros or 0 positive zeros, or 0 negative zeros or positive zeros, or negative zeros

5 Graph. ) = - - )

6 Begin b graphing the standard absolute value function f() =. Then use transformations of this graph to graph the given function. ) g() = - + )

7 Use the Leading Coefficient Test to determine the end behavior of the polnomial function. Then use this end behavior to match the function with its graph. ) f() = - - ) falls to the left and falls to the right falls to the left and rises to the right rises to the left and falls to the right rises to the left and rises to the right Solve the problem. 7) Solve the equation = 0 given that is a zero of f() = ), -, -,,,,, -, - For the given functions f and g, find the indicated composition. ) f() = + 7, g() = + (g f)() ) 9) f() = -, g() = - (f g)(),0 77, 9) 7

8 Use the verte and intercepts to sketch the graph of the quadratic function. 0) + = ( - ) 0) Find an nth degree polnomial function with real coefficients satisfing the given conditions. ) n = ; - and i are zeros; f() = 0 f() = f() = f() = f() = )

9 Identif the intervals where the function is changing as requested. ) Constant ) (-, -) or (, ) (-, 0) (, ) (-, 0) Evaluate the function at the given value of the independent variable and simplif. ) f() = - + ; f( - ) ) Use the Rational Zero Theorem to list all possible rational zeros for the given function. ) f() = ) ±, ±, ±, ±, ±, ±, ±, ±, ± ±, ±, ±, ±, ±, ±, ±, ±, ±, ±, ±, ±, ± ±, ±, ±, ±, ±, ±, ±, ±, ± ±, ±, ±, ±, ±, ±, ±, ± 9

10 Begin b graphing the standard square root function f() = given function. ) g() = Then use transformations of this graph to graph the ) Find the zeros of the polnomial function. ) f() = = -, =, = - 7 = 9 = - 7, = 7 =, = - 7, = 7 ) Find the zeros for the polnomial function and give the multiplicit for each zero. State whether the graph crosses the -ais or touches the -ais and turns around, at each zero. 7) f() = ( - )( - 7) 7), multiplicit, crosses -ais; 7, multiplicit, crosses -ais -, multiplicit, crosses -ais; -7, multiplicit, crosses -ais -, multiplicit, touches -ais; -7, multiplicit, touches -ais and turns around, multiplicit, crosses -ais; 7, multiplicit, touches -ais and turns around

11 Use snthetic division and the Remainder Theorem to find the indicated function value. ) f() = ; f() - ) Find functions f and g so that h() = (f g)(). 9 9) h() = + 7 f() = 9/, g() = 7 f() = /, g() = 9/ + 7 f() =, g() = 9/ + 7 f() = + 7, g() = 9/ 9) Graph the polnomial function. 0) f() = )