x 20 f ( x ) = x Determine the implied domain of the given function. Express your answer in interval notation.

Transcription

1 Test 2 Review 1. Given the following relation: = -6 - y Step 1. Rewrite the relation as a function of. Step 2. Using the answer from step 1, evaluate the function at = -1. Step. Using the answer from step 1, determine the implied domain of the given function. Epress your answer in interval notation. 2. Given the following relation: Determine h ( 1). h ( ) Given the following function: f ( ) = Determine the implied domain of the given function. Epress your answer in interval notation. 4. Consider the following quadratic function. g ( ) = -( + 6 ) 2 - Step 1. Find the verte of this function. Step 2. Determine the number of -intercept(s), then write the -intercept(s), any, of this function as ordered pair(s). Step. Graph this quadratic function by identying two points on the parabola other than the verte and the -intercepts. Also, write the two points as ordered pairs in the spaces provided. A: (, ) B: (, ) Test 2 Review Math Winter

2 5. Consider the following quadratic function. Reduce all fractions to the lowest terms. k ( ) = Step 1. Find the verte of this function. Step 2. Determine the number of -intercept(s), then write the -intercept(s), any, of this function as ordered pair(s) below. Step. Graph this quadratic function by identying two points on the parabola other than the verte and the -intercepts. Also, write the two points as ordered pairs in the spaces provided. A: (, ) B: (, ) 6. Consider the following quadratic function. Reduce all fractions to the lowest terms. h ( ) = Step 1. Find the verte of this function. Step 2. Determine the number of -intercept(s), then write the -intercept(s), any, of this function as ordered pair(s) below. Step. Graph this quadratic function by identying two points on the parabola other than the verte and the -intercepts. Also, write the two points as ordered pairs in the spaces provided. A: (, ) B: (, ) Test 2 Review Math Winter

3 7. The total cost of producing a type of car is given by C( ) = , where is the number of cars produced. How many cars should be produced to incur minimum cost? 8. A rancher has 600 feet of fencing to put around a rectangular field and then subdivide the field into 2 identical smaller rectangular plots by placing a fence parallel to one of the field's shorter sides. Find the dimensions that maimize the enclosed area. Reduce all fractions to the lowest terms. 9. The back of Tom's property is a creek. Tom would like to enclose a rectangular area, using the creek as one side and fencing for the other three sides, to create a pasture. If there is 60 feet of fencing available, what is the maimum possible area of the pasture? 10. Consider the following piecewise-defined function. f() = Step 1. Evaluate the given function at =. If the value is undefined, write "Undefined". Step 2. Evaluate the given function at = 6. If the value is undefined, write "Undefined". Step. Evaluate the given function at = 1. If the value is undefined, write "Undefined". 11. Consider the following piecewise-defined function. f() = Step 1. Evaluate the given function at = -1. If the value is undefined, write "Undefined". Step 2. Evaluate the given function at = -. If the value is undefined, write "Undefined". Step. Evaluate the given function at = 5. If the value is undefined, write "Undefined". 12. Determine algebraically the following function is even, odd, or neither. t ( ) = 1. Find and identy all of the intervals where the following function is increasing, decreasing, or constant. v ( ) = Determine algebraically the following function is even, odd, or neither. p ( ) = Test 2 Review Math Winter 2011

4 15. Consider the following function. u ( ) = Step 1. Identy the more basic function that has been shted, reflected, stretched, or compressed. Step 2. Graph this function by indicating how the basic function found in step 1 has been shted, reflected, stretched, or compressed. When necessary, indicate the units shted and/or the factor for streching or compressing. Step. Determine the domain and range of this function. Write your answer in interval notation or symbol notation. 16. Determine algebraically the following equation has y-ais symmetry, -ais symmetry, origin symmetry, or none of these. + y 2 = Consider the following function. 1 r ( ) = Step 1. Identy the more basic function that has been shted, reflected, stretched, or compressed. Step 2. Graph this function by indicating how the basic function found in step 1 has been shted, reflected, stretched, or compressed. When necessary, indicate the units shted and/or the factor for streching or compressing. Step. Determine the domain and range of this function. Write your answer in interval notation or symbol notation. 18. For f ( ) = 1 and g ( ) = - 1 Step 1. Determine the formula for ( f g )( ) Step 2. Determine the formula for ( g f )( ).. Test 2 Review Math Winter

5 19. For f ( ) = + 9 and g ( ) = Step 1. Determine ( f + g ) ( -1 ). Step 2. Determine ( f - g ) ( -1 ). Step. Determine ( f g ) ( -1 ). f Step 4. Determine g ( -1 ). 20. For f ( ) = + 2 and g ( ) = + 2 determine ( f g )( -1 ). 21. Find a formula for the inverse of the given function. G ( ) = Give a necessary restriction on the domain so the following function has an inverse function. k ( ) = 2. Solve the polynomial inequality 2 > Write your answer in interval notation. 24. Consider the following polynomial. p( ) = 5 2 ( + 7 )( + 9 ) Step 1. Determine the degree and the leading coefficient of p( ). Degree: Leading Coefficient: Step 2. Describe the behavior of the graph of p( ) p( ) ê as ê -Ù as ê ± Ù. p( ) ê as ê Ù 25. Solve the polynomial inequality ( + 1 )( - 2 ) 0. Write your answer in interval notation. 26. Use synthetic division to determine the given value for k is a zero of this polynomial. If not, determine p( k ). Is k a zero of this polynomial? p( ) = ; k = Use polynomial long division to rewrite the following fraction in the form q( ) + r( ) d( ) denominator of the original fraction, q( ) is the quotient, and r( ) is the remainder , where d( ) is the Test 2 Review Math Winter

6 28. Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms. Second-degree, with zeros of -2 and 6, and goes to -Ù as ê -Ù. 29. Given the following polynomial: H ( ) = Step 1. Identy the potential rational zeros. Step 2. Use polynomial division and the quadratic formula, necessary, to identy the actual zeros. 0. Use all available methods (in particular, the Conjugate Roots Theorem, applicable) to factor the following polynomial function completely f ( ) = Construct a polynomial function with the following properties: third degree, 4 is a zero of multiplicity 2, - is the only other zero, leading coefficient is. 2. Consider the factored polynomial f ( ) = ( + ) 2 ( - 2 ) 5 ( - 1 ). Step 1. Determine the degree and y-intercept (write the y-intercept as an ordered pair). Step 2. Determine the -intercept(s) at which f crosses the ais. If there are none, state "none". Step. Determine the zero(s) of f at which it "flattens out". If there are none, state "none". Test 2 Review Math Winter