f(x)= - x(x-2) (x+2)³

1) x-intercepts: - equate the factors to zero (zero product property)0 = x0 = x - 2 x = 20 = (x + 2)^3[cube root symbol] 0 = [cube root] (x+2)^30 = x + 2x = -2X INTERCEPTS: (-2,0) (0,0) (2,0)———2) y-intercept- Let x be zero.-(0) (0-2) (0-2)^30 (-2) (-8)0Y-INTERCEPT: (0,0)———3) Behavior of the Graph- use leading coefficient testDegree: 5 (odd) Leading Coefficient: -1 (negative)BEHAVIOR: Rises to the left and falls to the rightadditional informariona. Degree is odd and LC is positive— falls to left, rises to rightb. Degree is odd and LC is negative— rises to left, falls to rightc. Degree is even and LC is positive— rises to left and rightd. Degree is even and LC is negative— falls to left and right———4) Turning PointTp = n - 15 - 1TURNING POINT: 4———5) Multiplicity- check the factors and its degree. - multiplicity helps check the behavior of the graph to the x-axis. - x = 0 multiplicity of 1(x - 2) = 2 multiplicity of 1(x + 2)^3 = -2 multiplicity of 3additional information- use OCES mnemonic: Odd Changes, Even Samea. If the multiplicity is odd, graph crosses the x-axis.b. If the multiplicity is even, graph is tangent, touches, or bounces off the x-axis. ———6) Table of Values- i cant draw a table so just input these.- the x-intercepts have a y counterpart of 0. (1st row) x: -2, -1, 0, 1, 2(2nd row) y: 0, -3, 0, 27, 0———7) Graph-refer to attachment.

Answered by mikurosonya | 2024-10-20