f ( x ) = x Determine the implied domain of the given function. Express your answer in interval notation.
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1 Test Review Section.. Given the following function: f ( ) = Determine the implied domain of the given function. Epress your answer in interval notation.. Find the verte of the following quadratic function. Reduce all fractions to the lowest terms. g ( ) = Among all pairs of numbers ( y) such that 8 + y =, find the pair for which the sum of squares, + y, is minimum. Reduce all fractions to the lowest terms.. A rancher has 800 feet of fencing to put around a rectangular field and then subdivide the field into 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. 5. 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 90 feet of fencing available, what is the maimum possible area of the pasture? Section. 6. Consider the following piecewise-defined function. f() = 5 Step. Evaluate the given function at = -. If the value is undefined, write "Undefined". Step. Evaluate the given function at = -7. If the value is undefined, write "Undefined". Step. Evaluate the given function at = -. If the value is undefined, write "Undefined".
2 Section. 7. Consider the following piecewise-defined function. f() = + 8 if if Step. 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". Step. Evaluate the given function at = -. If the value is undefined, write "Undefined" Determine if the following function is even, odd, or neither. r ( ) = + 9. Determine if the following equation has y-ais symmetry, -ais symmetry, origin symmetry, or none of these. + y = 0. Determine if the following equation has y-ais symmetry, -ais symmetry, origin symmetry, or none of these. - = y -. Find and identify all of the intervals where the following function is increasing, decreasing, or constant. f ( ) = - ( + ) +. Consider the following function. f ( ) = Step. Graph this function by indicating how the basic function has been shifted, reflected, stretched, or compressed. When necessary, indicate the units shifted and/or the factor for streching or compressing. Step. Determine the domain and range of this function in interval notation.
3 . Consider the following function. g ( ) = - ( + ) + Step. Graph this function by indicating how the basic function has been shifted, reflected, stretched, or compressed. When necessary, indicate the units shifted and/or the factor for streching or compressing. Section.5 Step. Determine the domain and range of this function. Enter your answer in interval notation.. For f ( ) = + and g ( ) = Step. Determine ( f + g ) ( - ). Step. Determine ( f - g ) ( - ). Step. Determine ( f g ) ( - ). f Step. Determine g ( - ). Section.5 5. For f ( ) = + and g ( ) = - determine ( f g )( ). Section.5 6. For f ( ) = + and g ( ) = + determine ( f g )( ). Section.6 7. Find a formula for the inverse of the given function. V ( ) = 5 - Section.6 8. Find a formula for the inverse of the given function. f ( ) = 5 + Section.6 9. Find a formula for the inverse of the given function. g ( ) = Section Solve the polynomial inequality ( - ) ( + ) ( - ) > 0. Write your answer in interval notation.
4 Section 5.. Solve the polynomial inequality ( + ) ( - ) < 0. Write your answer in interval notation. Section 5.. 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 Section 5.. Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms. Second-degree, with zeros of -7 and, and goes to -Ù as ê -Ù. Section 5.. Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms. Third-degree, with zeros of -, -, and, and passes through the point ( 0 ). Section Given the following polynomial: Step. Identify the potential rational zeros. N ( ) = Step. Use polynomial division and the quadratic formula, if necessary, to identify the actual zeros. Section Consider the following polynomial function f ( ) = Step. Use all available methods (e.g., the Rational Zero Theorem, Descartes' Rule of Signs, polynomial division, etc.) to factor the above polynomial function completely. Step. Determine the degree and y-intercept (write the y-intercept as an ordered pair). Step. 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". Section Use all available methods (in particular, the Conjugate Roots Theorem, if applicable) to factor the following polynomial function completely, making use of the given zero, f ( ) = ; -i is a zero. Section Given the following rational function: f( ) = Step. Find equations for the vertical asymptotes, if any, for the rational function. Step. Find equations for the horizontal or oblique asymptotes, if any, for the rational function.
5 Section Solve the rational inequality. Write your answer in interval notation. + - Section Solve the rational inequality. Write your answer in interval notation. ³
x 20 f ( x ) = x Determine the implied domain of the given function. Express your answer in interval notation.
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