Chapter 6 College Algebra questions with verified answers

when doing (f o g) (-2), what do you find first? - answersg(-2) then plug in to f(x) to solve what do you do when you have a fraction within a fraction ex: 1/ (2/x+1) -4 - answersmultiply by the denominator of the extra fraction in this case, multiply by (x+1/x-1) to get rid of fraction domains for composite functions do not include (2 things) ex: f(x) = 1/x-4 and g(x) = 2/x+1 find f o g - answers1. final answer denominator can't equal 0 2. denominator can't equal 0 in the function you plug in [in this case, the denominator of g(x)] domains of square roots - answersset greater than or equal to 0 decomposition of composite functions - answers(f o g) (x) means f(x) is the outside and g(x) is the inside for example, in H(x) = /x+5 - f(x) = /x - g(x) = x+5 T/F exponents distribute to every term in parenthesis - answersTrue a^0 power always equals - answers1 exponential function - answersf(x) = Ca^x C is initial value of f(0) a is growth factor when x = 1 in an exponential function - answersf(1) = the base when x = -1 in an exponential function - answersf(-1) = reciprocal f(0) in an exponential function - answersf(0) = 1 domain of exponential function - answersall real numbers range of exponential function - answers(0, infinity) horizontal asymptote of exponential function f(x) = a^x - answersy= 0 transformation when exponent is negative - answersreflected over y axis transformation when base is negative - answersreflected over x axis transformation when number is multiplied to growth factor (exponent) - answershorizontal stretch/shrink one-to-one function - answersA function for which every element of the range of the function corresponds to exactly one element of the domain Finding an Inverse Function - answersinterchange x and y