Answer:
[tex] \displaystyle a = 6[/tex]
Step-by-step explanation:
we are given a absolute value function
[tex] \displaystyle f(x) = a |x| [/tex]
we want to figure out the value of a
since we are a point which is on the function we can figure out a by using the point i.e (1,6) this point tell us when x is 1 f(x) is 6 thus
substitute:
[tex] \displaystyle 6= a \cdot |1| [/tex]
absolute value of any integer is positive therefore,
[tex] \displaystyle 6= a \cdot 1[/tex]
simplify multiplication:
[tex] \displaystyle 6= a [/tex]
hence,
the value of a is [tex]\underline{\quad 6 \quad}[/tex]
