Using the properties of combinations of continuous functions, determine the interval(s) over which the function f left parenthesis x right parenthesis equals fraction numerator x squared minus 3 x minus 18 over denominator x plus 2 end fraction is continuous.A. left parenthesis short dash infinity comma space infinity right parenthesisB. left parenthesis short dash infinity comma space short dash 2 right parenthesis union left parenthesis short dash 2 comma space infinity right parenthesisC. left parenthesis short dash infinity comma space short dash 3 right parenthesis union left parenthesis short dash 3 comma short dash 2 right parenthesis union left parenthesis short dash 2 comma space 6 right parenthesis union left parenthesis 6 comma space infinity right parenthesisD. left parenthesis short dash 2 comma space 2 right parenthesis

Determine the interval(s) over which the graph of f left parenthesis x right parenthesis equals short dash x to the power of 6 minus 6 x to the power of 5 plus 12 x minus 2 is concave up or concave down. Concave up on left parenthesis 0 comma space 4 right parenthesis Concave down on left parenthesis short dash infinity comma space 0 right parenthesis union left parenthesis 4 comma space infinity right parenthesis Concave up on left parenthesis short dash 4 comma space 0 right parenthesis Concave down on left parenthesis short dash infinity comma space short dash 4 right parenthesis union left parenthesis 0 comma space infinity right parenthesis Concave up on left parenthesis short dash infinity comma space 0 right parenthesis union left parenthesis 4 comma space infinity right parenthesis Concave down on left parenthesis 0 comma space 4 right parenthesis Concave up on left parenthesis short dash infinity comma space short dash 4 right parenthesis union left parenthesis 0 comma space infinity right parenthesis Concave down on left parenthesis short dash 4 comma space 0 right parenthesis

Using the properties of combinations of continuous functions, determine the interval(s) over whichthe function f(x) = x²-3x-18 x+2 is continuous.A. (-∞,-2)U(-2,00)B. (-2,2)C. (-8,08)D. (-0,-3)U(-3,-2)U(-2, 6) U (6,0∞)

Consider the following function:f left parenthesis x right parenthesis equals open curly brackets table attributes columnalign left columnspacing 1.4ex end attributes row cell left parenthesis x plus 1 right parenthesis squared end cell cell i f space x less or equal than 3 end cell row cell short dash 2 x plus 22 end cell cell i f space x greater than 3 end cell end table closeDetermine if f left parenthesis x right parenthesis is continuous at x equals 3. If not, select the option with the correct reasoning as to why not.A. Continuous at x equals 3B. Not continuous at x equals 3 because limit as x rightwards arrow 3 of f left parenthesis x right parenthesis not equal to f left parenthesis 3 right parenthesisC. Not continuous at x equals 3 because limit as x rightwards arrow 3 of f left parenthesis x right parenthesis does not existD. Not continuous at x equals 3 because f left parenthesis 3 right parenthesis is undefined

Given limit as x rightwards arrow short dash 1 of f left parenthesis x right parenthesis equals 13 and limit as x rightwards arrow short dash 1 of g left parenthesis x right parenthesis equals short dash 5, evaluate limit as x rightwards arrow short dash 1 of left square bracket f left parenthesis x right parenthesis g left parenthesis x right parenthesis minus 19 right square bracket.A. limit as x rightwards arrow short dash 1 of left square bracket f left parenthesis x right parenthesis g left parenthesis x right parenthesis minus 19 right square bracket equals short dash 46B. limit as x rightwards arrow short dash 1 of left square bracket f left parenthesis x right parenthesis g left parenthesis x right parenthesis minus 19 right square bracket equals short dash 64C. limit as x rightwards arrow short dash 1 of left square bracket f left parenthesis x right parenthesis g left parenthesis x right parenthesis minus 19 right square bracket equals 46D. limit as x rightwards arrow short dash 1 of left square bracket f left parenthesis x right parenthesis g left parenthesis x right parenthesis minus 19 right square bracket equals short dash 84

The domain of the function f(x) is open square bracket, minus, 15, comma, 8, close square bracket[−15,8] and the range is open square bracket, 4, comma, infinity, right bracket[4,∞). Using interval notation, find the domain and range of g, of, x, equals, minus, f, of, xg(x)=−f(x).