College Algebra Essentials 1st Edition by Julie Miller solution manual

square root function: f(x)= sqrtx cube root function: f(x)= 3sqrtx reciprocal function: f(x)= 1/x greatest integer function y= -f(x) reflection about the x-axis y= f(-x) reflection about the y-axis vertical stretch y= af(x) multiply each y coordinate by a horizontal compression a>1: divide each x coordinate of y= f(x) by a horizontal stretch 0<a<1: divide each x coordinate of y= f(x) by a one-to-one function a function is one-to-one if for any values a cant = b in the domain- can determine this using the horizontal line test finding the inverse of a function quadratic function the porabola opens up if the leading coefficient a>0 the porabola opens down if the leading coefficient a<0 the standard form of a quadratic function the vertex of a porabola: (h,k) e natural base vertex formula revenue equation Revenue= Price x Quantity R=PXQ the right hand end behavior finishes up if a>0 the right hand end behavior finishes down if a<0 even degree end behavior if the degree n is even the graph has the same left and right hand end behavior- it starts and finishes in the same direction long division quadratic formula compound interest formula simple interest formula distance formula D=R X T complex numbers discriminant formula if D> 0: 2 real solutions if D<0: 2 non-real solutions if D=0 : exactly 1 solution factor by grouping inequality signs when the inequality sign changes if you multiply or dividing both sides of the inequality by a negative number it changes the direction of the sign when the inequality sign does not change if you add or subtract both sides of the inequality solving a compound inequality with and it will involve the word and- first solve each inequality separately- then find the intersection of the two solution sets interval notation of compound inequalities with the word or will have the union sign U greater/ less than or equal to filled in circle greater than/ less than open circle quadrants midpoint formula distance formula