Alternative transcript:

radical if In is odd, leaving possibility of f(x) = a^²√√ -(x-n) + k if n is even. • to graph: 1. find vertex (minimum or maximum) 2. apply transformations in correct order vertical in PEMDAS, norizontal in reverse PEMDAS 3 have at least 3 points SOLVING RADICAL EQUATIONS to the goal is to eliminate the radical / root sign by: isolating the radical 2. ruising each side of the equation to the root's power SYSTEMS Calgebraically and graphically) • solve algebraically first, then graph to find extraneous * note the difference between radical FUNCTION and radical EXPRESSION (includes negatives) + ± √√√ ALWAYS CHECK FOR EXTRANEOUS SOLUTIONS DIRECT, INVERSE AND JOINT variation) • direct= y = kx _inverse = y = k/x • joint: multiple relationships in one equation - to figure out, solve for y = ? ↳ when given a table, graph it first then find equation for joint variations: if varies directly it goes with k in the numerator and if inverse on the denominator 2 ✓ ● UNIT four STUDY GUIDE RATIONAL FUNCTIONS (graphing) rational function: y = (?)/(?) x (also called reciprocal) 4 :a/x = · . . . a Y=x-h if a o 5 y= no reflection & if a ≤o, x-axis reflection 1 lal is the vertical stretch, moves away from origin +/- in denominator: horizontal shift / vertical asymptote +/- outside: vertical shift / horizontal asymptote a LP usual transformations: V = (x-h) + K K asymptotes: not included vertical asymptotes @ x=h! {domain: (-∞o, h) u (h,00)} LP horizontal asymptotes @y= KV ² range: (-∞, k) U(K,~0)} ↳ for graph (ax² + x² ..) / (ax" + x "- '...) : 3-1 • if men, the line y=0 is a norizontal asymptote • if m= n₁ (a/b) line is a norizontal asymptote • if man, no horizontal asymptote → has a POLYNOMIAL ASYMPTOTE equal to the quotient (do polynomial or synthetic division) • if just a line, called oblique / stant asymptote finding holes: factor numerator & denonominator, factors that cancel out are noles (o on graph) → find y-value by removing cancelled factors and plugging in the x-value • not every graph will have a hole SYSTEMS INEQUALITIES (rational) & systems: find a common denominator and solve as normal • inequalities: 1. get 0 on one side 2. factor & find domain 3. sign analysis & graph 4. declare solution