3. graph the step function and find a( 5 )\na(x)=\\left|\\begin{array}{ll}2 & 0<x \\leq 3 \\\\ 4 & 3<x \\leq…

3. graph the step function and find a( 5 )\na(x)=\\left|\\begin{array}{ll}2 & 0<x \\leq 3 \\\\ 4 & 3<x \\leq 6 \\\\ 6 & 6<x \\leq 9\\end{array}\\right.\na(5)= \ndomain:\nrange:

3. graph the step function and find a( 5 )\na(x)=\\left|\\begin{array}{ll}2 & 0<x \\leq 3 \\\\ 4 & 3<x \\leq 6 \\\\ 6 & 6<x \\leq 9\\end{array}\\right.\na(5)= \ndomain:\nrange:

Answer

Explanation:

Step1: Determine the value of ( A(5) )

Since ( 3<5\leq6 ), use the function ( A(x) = 4 ) for ( 3 < x\leq6 ). So ( A(5)=4 ).

Step2: Find the domain

The domain is the set of all ( x - ) values for which the function is defined. The intervals for ( x ) are ( 0 < x\leq3 ), ( 3 < x\leq6 ), and ( 6 < x\leq9 ). Combining these, the domain is ( (0,9] ).

Step3: Find the range

The range is the set of all ( y - ) values (outputs of the function). The function has values ( 2 ) (for ( 0 < x\leq3 )), ( 4 ) (for ( 3 < x\leq6 )), and ( 6 ) (for ( 6 < x\leq9 )). So the range is ( {2,4,6} ).

Answer:

( A(5)=4 ), Domain: ( (0,9] ), Range: ( {2,4,6} )